It's proven that he didn't die in the bunker [to me - read that long article from Burner.me; and other information sources - there were several shows about it on Red Ice Radio and elsewhere.]

It could be proven she is his daughter, [or not], but that's unlikely to happen.

If the public could do verified DNA checks on public figures, that would be great.

But it's too easy to falsify or to do a "switcheroo" with the biological material. Or just to have the Mass Media lie, per the usual.

Also, with proof, different people have different standards of what they will accept as "proof."

Everyone has to prove something [or not] for themselves. No one can prove anyting for anyone else; they may be unable to see what you see. You have to see, and verify it, for yourself. Someone else may accept your reasoning, logic and data; or they may take exception, and disagree.