|St. Peter and St. Paul Lavenham|
These two authors had apparently not seen the Paine entries in the parish records of Lavenham, they did not know the existence of the Lavenham Paines. They did not have the baptismal or marriage records of the Paine's of Lavenham, did not know they lived, married and died there, they did not know the name Agnes Neves or the names of the Paine siblings who did not immigrate to Massachusetts.
What most people seem to have done is taken the Paines of Lavenham, their baptisms and deaths and sorta said they were born in Nowton Parish of Lavenham, or some other mishmash of names. But Nowton is Nowton and Lavenham is Lavenham, two entirely different places, each with it's own parish church.
who they weren't
William of Nowton married in 1602. He wife's name was recorded in the 1612 Visitation of Suffolk, she was Elizabeth Sparrow of Standsfelde. They married in the parish of Rede, which is only a few miles south of Nowton. 
William of Nowton's father, Anthony, died in 1606. Although not his heir, he made bequeaths to his son William in his will. He also named his one year old granddaughter Anne.  In 1606 William of Lavenham had five or six children and his daughter Anne was 18 years old. William of Nowton died in November of 1648, his wife had died the previous April. William of Lavenham died in 1621, his wife Agnes died in October of 1645. All the Paines of Nowton were buried in Nowton. William of Nowton seems to have had a son William, baptized in 1605 in Barnham, but as he was not named in his grandfather's will, it is presumed that he was dead.
A side by side comparison of the two families shows that the Lavenham Paines were baptized, married and buried in Lavenham. The Nowton Paines were baptized in Bury St. Edmunds and buried in Nowton. So, I don't know what else to tell you. If you're still not convinced, can I ask a favor? Many people are under the assumption that if a man was "Lord of the Manor" then his title was 'Sir'. This is not true. In order to be called 'Sir', a man must be Knighted. Anthony Paine and his sons were not Knights, they were referred to as Gentlemen, and therefore they were called 'Mr.'. I have seen multiple ancestry trees which have the Paines given the title of Lord and Lady Paine, and Sir William Paine. This is incorrect. So, if your going to use an incorrect pedigree, could you at least do it correctly. :)
Richard the eldest son named in Thomas' will died in late 1575. He identified himself as a Clothier of Boxted. He named in his will, written in January of that year, his wife Margery. She was dead by the time of the November probate. He also named his sons Richard, Thomas and John. He mentions Marion, Joane and John Firman (presumably the Firmans are related). Richard also leaves four nobles to the children of William Paine, his brother. 
move to lavenham
William, son of Thomas and brother of Richard had three known children: William Jr., Thomas and Agnes. The name of William Sr.'s wife is unknown as are the birth dates of the children. The three children are known to have lived in Lavenham. The parish register begin in 1558 so we can only trace the family to that time. A William Paine Sr. died in 1587 and a William Paine died in 1583, either of these could be him. I think he was the William who died in 1587.
In 1559 a birth of a Thomas Paine was recorded in the Lavenham parish records. He was, most likely, the son of William Jr., who was presumably now married and living in Lavenham, some seven or eight miles from Boxted. William's brother Thomas married Agnes Wyatt in 1561 and their sister Agnes married George Seargentson in Lavenham in 1565.
William Jr. and his wife, possibly the Widow Joane Payne who died in 1594 had at least two sons, the Thomas born in 1559 and a son William III. This William is the one who married Agnes Neves of Lavenham in 1584. The births of their children are recorded in the Lavenham parish records beginning with Elizabeth, my ancestor, who was born in 1586. William Jr. died the following year in 1587. William III, called William Payne the Elder in the records, died in 1621. His son William and daughters Dorothy, Phoebe and Elizabeth are the siblings who immigrated to Massachusetts. When Agnes died she left her home in Lavenham Market to her daughter Susan and left money to her son Richard, both of whom remained in England. Agnes was buried in the Lavenham churchyard. 
paine meets paine
In an odd twist of fate, the two William Paines, one of Lavenham and the other of Nowton, may have come face to face. On 6 October 1634, William Paine, 37, clothier of Lavenham, was deposed in a court case involving his brother Richard. His deposition was taken at the Greyhound Inn in Lavenham before two commissioners; Sir Robert Crane, Baronet and William Payne, Gentleman. Were these the two Williams who are confused today? I think they were?  Another interesting thing about this court case is that Richard Paine stated that he had gone to Bury St. Edmunds, "a long way off" where he "was a stranger." Anthony Paine had owned many houses and lands in Bury and he had been one of the leading men there. If Richard was his grandson, he would have been known to men in Bury and not thrown in jail.
William Paine's family members obviously lived, married, died and were buried in Lavenham. They had no connection to Nowton Manor. Below is my side by side comparison of the two families. It's a bit squished in this view but you might find it helpful.
Paine of Lavenham
Paine of Nowton/Bury St. Edmunds
Thomas Paine of Boxted died
Mr. Henry Paine, Lawyer of Bury St. Edmunds, buys Nowton for 648 pounds
John Paine s/o Anthony, baptized at St. Marys Bury St. Edmunds
Thomas s/o William (1) Paine, bp. St. Peter St. Paul Lavenham
This is the brother of William (2)
Anne d/o Anthony Paine, bp. St. Marys Bury St. Edmunds
Thomas Paine m. Agnes Wyat St. Peter St. Paul Lavenham
Margaret d/o Anthony, bp. St. Marys Bury St. Edmunds
Thomas s/o Anthony, bp. St. Marys. Bury St. Edmunds
Agnes Paine m. George Sergeantson St. Peter St. Paul
Agnes is sister of William (1) and Thomas
William s/o Anthony, bp 2 Dec at St. Marys Bury St. Edmunds
Henry Paine, Lord of Nowton, buried at Nowton 26 July
Thomas s/o Anthony admitted to Caius College, Cambridge at age 16
Joane Wright Servant of William Paine buried at St. Peter St. Paul Lavenham, probably a servant of William (1)
William Paine m. Agnes Neves St. Peter St. Paul Lavenham
This is William (2)
Elizabeth d/o William Paine bp. St. Peter St. Paul Lavenham
William Paine Sr. buried at St. Peter St. Paul Lavenham
this is the father of William, Thomas and Agnes
Anne d/o William (2) bp. St. Peter St. Paul Lavenham
Judith d/o William bp. St. Peter St. Paul
Susan d/o William bp. 22 June St. Peter St. Paul
Susan d/o William buried 1 June St. Peter St. Paul
Susan d/o William bp. 1 April St. Peter St. Paul
Jane d/o William buried
William and Richard s/o William bp. St. Peter St. Paul
John Paine, s/o Anthony buried at Nowton 28 October. John was also the heir of Anthony. Because of his death his son Anthony became the heir of Anthony (1)
Anthony s/o John Paine (deceased) admitted to Caius College Cambridge age 16
Francis d/o William bp. 20 July St. Peter St. Paul
Francis d/o William buried 12 August St. Peter St. Paul
William Paine s/o Anthony m. Elizabeth Sparrow at Rede, Suffolk
Martha Paine w/o Anthony Sr. buried 28 June Nowton
William's daughter Ann is now 18 years old
Elizabeth Paine m. William Hammond 9 June St. Peter St. Paul
(Ann d/o William born, no parish record found)
William and Agnes have six living children: Elizabeth, Ann, Susan, Phoebe, William and Richard.
Anthony Paine buried 4 March at Nowton. He wrote a will and named, leaving his estate to Grandson Anthony (2). He also names his son William and William's daughter Anne.
William Paine pays 3,000 pounds to his Nephew Anthony for Nowton
William Paine holds his first court at Nowton
Visitation of Suffolk: William Paine m. Elizabeth Sparrow, daughter Ann age 7, not other children named.
Anne Paine m. Richard Neve St. Peter St. Paul
Phebe Paine m. John Page St. Peter St. Paul 5 June
William Payne the Elder buried 9 June St. Peter St. Paul
William hold his last court as Lord of the Manor of Nowton. He sold the manor to Sir Daniel de Ligne.
William s/o William Paine bp. 9 Nov. St. Peter St. Paul
No marriage record for this William, he m. by 1623 to Anna
Anne Neve Paine wrote her will on 8 December. She named only her daughter Susan and her son Richard
Anne (Agnes) Neve Paine d. buried at St. Peter St. Paul Lavenham
William Paine, sometime Lord of the Manor of Nowton, buried at Nowton. He requested to be buried next to his wife in the chancel.
 Albert W. Paine, Paine Genealogy, Ipswich Branch, (Bangor, Maine: O. F. Knowles, 1881), 51, digital images, Hatitrust (babel.hatitrust.org : accessed 5 February 2016).
 Henry D. Paine, Paine Family Records, a journal of genealogy and biographical information respecting the American families of Payne, Paine, and Payn, (Albany : J. Murrell, 1883), 177, digital images, Hatitrust (babel.hathitrust.org : accessed 5 February 2016).
 William Harvey, Robert Cook, John Earl Raven and Walter Charles Metcalf, "The Visitation of Suffolk Made by Hervey, Clarenceaux, 1561, Cooke, Clarenceaux, 1577, and Raven, Richmond, Herald 1613, with notes and an appendix of additional Suffolk Pedigrees, (Exeter, William Pollard, 1882), 157; digital image, Internet Archive (https://archive.org/stream/visitationsofsuf00harvuoft#page/156/mode/2up : accessed 8 October 2015).
 Henry D. Paine, Paine Family Records, 177.
 Elizabeth French, "Genealogical Research in England," The New England Historical and Genealogical Register, Boston, MA,The New England Historical Genealogical Society, 1915, 69, pgs. 251-252; digital images, American Ancestors (http://www.americanancestors.org/databases/new_england_genealogical-and_historical_register : accessed 4 Oct 2015).[ Contains the Payne births, deaths and marriages from the parish records of Lavenham.]
 G. Andrews Moriarity, "Genealogical Gleanings in England V," The New England Historical and Genealogical Register, Boston, MA, The New England Historical Genealogical Society, 1925, 79, pgs. 82-84; digital images, American Ancestors (http://www.americanancestors.org/databases/new_england_genealogical-and_historical_register : accessed 4 Oct 2015).
 G. Andrews Moriarity, "Genealogical Gleanings," 84.
 G. Andrews Moriarity, "Genealogical Gleanings," 84.
 Author unnamed, "Gleanings from English Records," The New England Historical and Genealogical Register," 103 (1949) 183-185, digital images, American Ancestors (https://www.americanancestors.org : accessed 5 February 2016). [court case involving Richard Paine and his brother William Paine, both of Lavenham.]