Earlier quoted context omitted.
A good start would be to require that claimants must verify their real identity. The claim in this case was made by an apparent pseudonym and their address is fictional. Both should themselves be reason to reject the claim. The fact that anyone apparently can submit claims to Google under false names seems insane to me.
Who decides what counts as a "real identity"? Fictional address, sure: that would, as I understand, be some kind of fraud, and can reasonably be prohibited if there's a mechanism to do so… but then you run into the problem that not everyone has an address.
Notaries do this all the time often for free or for a fairly minimal fee.
The solution doesn't have to be perfect to be better.