Re: Proof of ownership?
It's hard to know whether they know it. If for whatever reason you haven't told your child who their biological father is then you're hardly likely to tell some random researcher, are you?
In England if you're the husband of a woman who has a baby, and you want to be the father, then you are the father, pretty much, as I understand it, even if you've been separated from the mother for years. This can be an unpleasant surprise for the biological parents.