That's Kafkaesque. We're not talking about SEO here, just simple proof of identity. If they require something sane like ID, they could simply say so. If they need something insane, or have no process at all for proving identity, then this is no excuse.
In this case, a more likely explanation might be "Google won't do this because it would put you in a position to obligate them to do something else". There isn't really a risk of enabling scammers to issue false DMCA takedowns; as you note, that issue is resolved by requiring proof of ownership.
If that were true, how would the judge know who to rule for? Are you saying that anyone can become the owner of any intellectual property simply by filing a lawsuit?
Not all intellectual property is the same. Trademarks have to be registered, patents have to be filed, but copyright is automatically granted by law whenever someone creates a work.
Trademark issues are therefore really simple: is the user of the trademark the one who has it registered or not?
But copyright holders don't have any standard, obvious evidence they can point to that shows it's really their copyright. They can file a DMCA, in which case companies normally just assume the complaint is accurate - but if the party on the other end objects, the case has to go to a judge who will determine who actually has the copyright and if infringement occurred.
