I have found sometimes that if it appears someone doesn't have a tree, they 'do' have a tree, it's just that they haven't attached their DNA test TO a tree. They may have two or three trees. Then it's an exercise in diligence to figure out which tree it might be, OR contact them (and wait for an answer) to find out which tree it might be, and which person (because it might be the spouse rather than the home person).
Like your "dog in a manger" expression. Made me smile.