This is a follow-up question to Using DNA to link individuals after a name change
My cousins and I are pretty sure my great-great grandfather, Everett T Malcom, changed his name when he moved west. We have a compelling theory that his birth name was Mark Ellsworth Templin, and his parents were John Wesley Templin and Jane Stokes. My great-uncle (Everett's grandson) took a DNA test, and it matched with several descendants of John Wesley Templin and Jane Stokes as "third cousins", with "extremely high" confidence (according to ancestry.com).
My concern is that the DNA testing companies only let me see the trees for people who are genetic matches. There doesn't seem to be a way to find out if there are other descendants of John Wesley Templin who are not matches.
Doesn't this create a significant risk of confirmation bias?
If so, how do I counteract this?
Is there a site that will let me view DNA info for people whose family trees match, instead of the other way around?