I don't think they are just comparing trees. Many of my matches have no matching surnames, so they must be showing matching DNA. Their ability to match surnames leaves much to be desired, though. I don't see that it could give you a "match" unless you have two people with the exact same name and close to same date of birth. My only matches have been with trees that both have our common ancestor. I had a surname match for one person and knew that surname could be traced back to a single ancestor in that area. I was able to connect her ancestor with my ancestor in MY tree, but because she does not show our common ancestor, Ancestry cannot make the match.
Depending on how long your White family has bee in America the match may not be so funny. What is the relationship they predict for you and the other member? White it a very common name. Do thy give you any other surnames in common?