Under the presumption of innocence, the legal burden of proof is thus on the prosecution, which must present compelling evidence to the trier of fact (a judge or a jury). If the prosecution does not prove the charges true, then the person is acquitted of the charges.
That should be "considered innocent by the legal system". People are still free to come to their own conclusions--and act on them--even without a jury rendering a verdict.
Rather famously, for example, OJ Simpson was acquitted by a jury of murdering his wife. But most people these days would agree with the statement that he murdered his wife.
Which is what matters when determining sentences.
> People are still free to come to their own conclusions--and act on them
People are definitely not free to act on their conclusions. That's vigilantism, what the comment above was referring to.
There can be whatever reason he wasn't convicted, it doesn't change the fact that he wasn't and presumed innocence is the legal default.