Very true. I think many that are not in the scientific community do not understand that almost all papers in top journals are given "revise and resubmit" status, so people can fix small to large issues before being reviewed again. This process makes the paper more understandable, not just to the reviewers, but to the community at large. It is not a perfect process, but definitely one that has improved writings as a whole.

I’ve never heard of a paper that was accepted without revisions after peer review. There’s always some (thoigh frequently many) requested changes, but never once have I seen three reviewers all sign off without having a single suggestion.

It seems almost inherent to the process. I don't read or write journal articles. But I'm sometimes asked to be a reviewer on a book proposal and I fairly frequently review docs of various types at work.

If I'm just one peripheral person on a long list I might read quickly through and say "Looks fine to me." But if I'm really reviewing something, I almost feel that I'm expected to at least find some nit-picks--as well as anything really substantial of course. It's pretty rare that I will be "No comments" on a first-pass review.

The insulin-antigen one did claim it was not proven true. Is that close enough to 'wrong'?

I can't really judge, but by the sounds of it the paper didn't provide enough evidence to prove that it was true, or at least didn't make it obvious that it was true. They even admit that the data presented was "suggestive" that it might be true.

This is something you see all the time. Someone does a limited experiment, gets the result they where hoping for, and then get super excited and carried away and claim that their entire thesis has been proven true. I've rejected (or rather sent back for extensive revision) papers myself based on this, even when my gut feeling was that their conclusion was probably correct. Often the paper comes back with a more moderated conclusion and then gets published without a problem.