Ann, not my direct line, but at https://services.dar.org/Public/DAR_Research/search/?Tab_ID=1 enter Ancestor Number A119449 and take a look at the comments and information on Colonel John Walker, b.1728. Specifically:
EL - JAMES SON OF PATRIOT DIED BEFORE 1826.
JAMES REUBEN WALKER A119428 WHO MARRIED SARAH MCHERD NOT SON OF THIS PATRIOT. SEE DATACF 3/2010
If James Reuben Walker was not the son of Walker-1098, the myth probably began with the 1930 book, Revolutionary Service of Col. John Walker and family, and Memoirs of Hon. Felix Walker, by Clarence Griffin: https://digital.ncdcr.gov/digital/collection/p249901coll37/id/29267.
William Walker, Walker-15948, is my line, through his brother James, Walker-17042. Reuben Walker was added 4 March 2020 as a son to William, but I have no information in my collection on that family to corroborate it. However, on the FreeSpace page at https://www.wikitree.com/wiki/Space:Walker-15949_Research, in the section headed "Subject 3: Walker Surname Project at FTDNA," note that there is a purported descendant of Reuben Walker who is in the same yDNA grouping as William Walker's father, Thomas Walker. That alone doesn't provide any correlation because information about the earliest known ancestor is self-supplied by the test-taker with no reference citations.
One other curious thing is that, in the Pension Roll of 1835, Volume III, Burke County, North Carolina, we find a Reuben Walker who served in the North Carolina militia, placed on the pension roll 21 Sep 1833, and who is recoded as being 74 years old. That places the date of birth at c. 1761, not 1757 as the profile shows. Of no real additional help is a few words in Vol. 2 of "Abstract of Pensions of North Carolina Soldiers of the Revolution, War of 1812 & Indian Wars": https://www.ancestry.com/sharing/30421786?h=5ada60. This corresponds to the 1835 pension roll info, shows a 1760 birth, and shows an 1836 application for transfer of pension benefits to Knox County, Tennessee, as "most of his children are now living in Tennessee."
To further confuse the matter, there are some public trees (but we know how unreliable those can be) who show that the Reuben Walker who died 3 Jul 1841 was the son of Joseph Rutherford Walker, not Col. John or William Walker. And Find a Grave--though without a photo of a gravestone or a corroborating source citation--shows Reuben as dying in 1836, not 1841: https://www.findagrave.com/memorial/171584930/james-reuben-walker.
There are no verifiable sources on Reuben's profile, so it seems difficult to tell if Reuben (or James Reuben) was the son of either man.