When ancestry searches are made back into the 16th century and beyond, even professional genealogists cannot agree - please do not ask for more sources - most cannot be proven.
The parentage of John Adams is not the focus here - his burial location is. He is believed by many researchers to be the second son of John Adams "of Fenne" and Catherine [Katherine] Stebbing. (Some researchers name an Alyce [Alice] as a wife of John Adams "of Fenne").
John was christened at Barton St. David Church on 4 January 1508.
This John Adams, [circa 1500/05], lived all of his adult life at Barton St. David, and is the earliest found (at this date) member of this Adams' family line. He is on the Muster Roll for the tything of Barton in 1539 as "able bylman fyndyng harnys". He was charged with the duty of providing one "bowe" (bow) with a sheath of arrows as a tax on his goods. 
Adamses of Somersetshire, England and Braintree, Mass., Compiled by J. Gardner Bartlett for Edward Dean Adams, privately printed, New York, 1927.
Dorset Pilgrims, by Frank Thistlethwaite, Published by Heart of the Lakes, Interlaken NY, 1993.
Married Margerye Squire, 1529, Barton, St. David, Somerset, England.
His known ancestry begins with ARNULPH, Bishop of Metz, France, born before the year 600, died 631 A.D. and decends 5 generations to CHARLEMAGNE, Emperor of the West, born 2 April 742, who was King of the French and Emperor of Rome.
Charlemagne begat Louis I (The Pious, King of France) and his son, Charles II, King of France begat a long line of counts, dukes, barons, etc. until came Sir JOHN A P ADAM, Knight.
At this, the 31st generation, John Adams' great great grandfather, Sir John A P Adam, dropped the prefix "A P" and added "s" to Adam. Then there were two more John Adams's before we get to where we now are - 1502!
Dozens of John Adams's were to follow, making my 2010 geneology a living nightmare.
No gravestone or marker remains
Margerye Squire Adams
1504–1572 (m. 1529)