Not quite sure what you're getting at with "authenticated distributed data," but records that came from a PDS are signed by the PDS. The signatures are there to enable untrusted mirrors to be used for distribution. There's a downside: you can't really disavow a post. But that doesn't seem to be the purpose of the signatures? It's more of an unfortunate side-effect.

In practice, this can be annoying and there are alternatives for people who write software that doesn't bother to check signatures.

Relying on https alone means you kinda have to get the data from the original website to know that it's authentic, and you can't prove it to anyone else other than by sending them the URL so they can check for themselves. (I mean, technically. In practice, people will trust quotes or screenshots even though they can be faked.)