No, definitely not. I have no inherent reason to trust the people working at the Internet Archive over let's say close friend. For me trust is always a human to human concept, and no amount of tech or institutions will change that.

The more people I hear making a claim, the more I'm likely to deem the claim(s) as true. This is even true regarding the claims that cryptographic algorithms have the properties that make them useful in these contexts. I say this as someone who has even taken graduate level classes with Ron Rivest.

I'm not sure what will happen in a court. I imagine the more people that start making claims using cryptography as part of the supporting evidence, the more likely people will start to trust cryptography as a useful tool for resolving disputes about the veracity of claims.

So you would not get any value from multiple people making such claims?