The general notion of "innocent until proven guilty" is simplistic even when applied to just the legal system. Even in criminal court you only have to establish guilt beyond a reasonable doubt. You do not have to "prove" guilt to the same degree of confidence as, say, the Higgs boson.

This means that a small number of innocent people are convicted every year. This is unfortunate, but less bad than the alternative — the only way to guarantee no false positives is to never convict anyone.

The legal system, like any other justice system, is about finding an appropriate balance between false negatives and false positives.

when we talk about proven in the empiric sense a margin of error is always expected. but what "innocent until proven guilty" guarantees is that best efforts were made to make sure that someone is really guilty. Trial by social media cannot reasonably offer such guarantees.

Also, I presume you would agree that the police and by extension the court have better means than your average newspaper for determining guilt.

While the legal system might have more power than the average newspaper, that doesn't mean that it is more effective at determining guilt.

I was raped 10 years ago when I was a teen. There is no evidence of the crime. No court is going to convict my rapist.