John Barnes, of Plymouth Colony - Descendent of George Barne, Lord Mayor of London?

It’s not a possible ancestral link. I’ll go through why in the next post, but wanted to share this comment first from Plymouth Colony researchers:

“ The following is purely the speculation of one of the researchers, some based on fact, and some based on wild imagination. This should not be used for purposes of reference or research:

Given to both "civil" and "less civil" interactions, John Barnes dealt with all walks of life in Plymouth Colony. He was a businessman in the truest sense, even in today's terms. He had enough gumption and gall to poison a snake, and still have some left over to pass around the room (who else would "pet" a bull; granted, the bull "stroked" him back). When refinement was demanded, Barnes was there to muddle through, but he was also a man given to the "darker byways" of colony life,(26) a lover of drink and pipe. Barnes gives us a glimpse at a Plymouth reality that our eyes have not been trained to see.”

http://www.histarch.illinois.edu/plymouth/BARNES2.htm

So the Geni parents for john Barnes are currently seen as William Berners of Thoby & Dorothy Barnes With no sourcing.

I see at https://www.familysearch.org/tree/person/details/GQ8R-TY7
A fellow called lWilliam Edward Barne Sir, Knight, Lord Mayor of London,17 July 1580 – 24 March 1629” married to a Dorothy Hansard, with 3 sets of parents, including Anne Sandys.

And Anne Barne did have a son Sir William Barne, Kt., of Woolwich who did marry a Dorothy - but they didn’t have a son John.

“ 1. Sir William Barne5 of Woolwich. Knighted at Greenwich 29 June, 1618. Aged 26, 7 May, 1619. Living and married before 16 May, 1632, when he is named in his sister Anne Lovelace's will. Married Dorothy Manwood, daughter of Sir Peter Manwood of St. Stephens, Canterbury, K. B., by Francis, daughter of Sir John Harte. Issue four sons. See also Visitation of Kent, 16x9 (Harl. Soc. lxii; 144).”

(That’s from http://books.google.com/books?pg=PA123&dq=george+barne,+lord+ma...)

Awesome, thank you for the thorough response!