I manage the Find-A-Grave site for Nancy Jarrell Madison that you found using information from my research (with many thanks to Natalie Herdman, who originally created the site and generously contributed the photo and inscriptions).
Nancy’s correct birth and death dates are not yet confirmed. We only know her exact birth date by subtracting her age on the grave marker from her death date, but we have two conflicting death dates--her grave marker says she died May 11, 1875, and a Cincinnati Daily Gazette obituary says May 15, 1875. So until Nancy's death date is verified, there are two alternate sets of dates:
Born May 26, 1789 - Died May 11, 1875 (using death date from the grave marker) OR Born May 30, 1789 - Died May 15, 1875 (using death date from the obit)
As for William Madison, his Find-A-Grave website has a number of errors. The information did not come from his grave marker, because none exists. There is no graveyard at William’s former estate in Madison Co, VA, where he died, so it is presumed that he is buried several miles away in the Madison Family Cemetery at Montpelier, Orange Co, VA, even though no marker was found.
The first error in William's information is his name. As I explained in my post earlier today to Helen, William Madison had no middle name or initial, even though the erroneous name "William Taylor Madison" or “William T. Madison” has been copied over and over on the web for years. Instead, all William’s personal and official documents, including how he wrote and signed his own will, say only “William Madison.” (For full documentation that proves he had no middle name/initial, see the Montpelier Foundation’s Madison Family genealogy that I’m linking below.)
In addition to William’s name, his Find-A-Grave site has his birth date, death date, and place of death wrong. (Actually, Nancy herself is the source of the death date of July 20 in an 1853 pension statement. But Chapman documents significant overriding proof for July 19 instead.) William and wife Frances Throckmorton had 11 children, not just the 5 on the Find-A-Grave site.
This is from the Madison Family Genealogy by Thomas Chapman at the Montpelier Foundation:
WILLIAM MADISON Born: 1 May 1762 at Montpelier, Orange County, Virginia Baptized: 23 May 1762 in Orange County, Virginia. Died: 19 Jul 1843 at Woodberry Forest, Madison County, Virginia Buried: Madison Family Cemetery