dna genetics has made amazing strides.
I am sure this Houston based lab was FTDNA. They, Ancestry, and 23/Me all have databases, that catalog, who not only who you are related to, but how close. This based on strand cM match lengths. (centimorgan).
In my case, I have catalogged all 4th cousin and closer matches so extensively, that in 90% cases on matches, I can tell generally what part the family a new user is, as related to me, based on triangulaton of all the users prior matches to.
Once you have that data, and it pares down real easily, you with a bit of research can likely find the common ancestor. I've helped dozens with this, in this part of their research
Surprised law enforcement has utilized methods like I have use to ID all "John, Jane, Does and Miss Nobody's". Wouldn't be that actually hard, unless they are immigarants, or from a narrow tree'd family.