There is little or no difference in meaning, and only a subtle difference in nuance.
Both "was proved" and "has been proved" are in the passive tense, which implies the result of action by some (possibly unstated) subject. For example:
active: The psychic claimed the latest reports proved her predictions to be correct.
passive: The psychic claimed her predictions were proved correct (by the latest reports).
So a sentence like, "... he was proved to be innocent," implies that someone did the proving.
"Proved", by itself, implies a condition or result. While in most cases we can assume some kind of evidence or human action, the nuance is simply, "this is how it is" or "this is what happened".
As used in your examples:
He proved to be innocent (= "the end result (of some unstated process) was that he was innocent")
Her biopsy proved to be harmless (= "the test reached the conclusion that the cancerous growth was harmless")
Again, both have more or less the same meaning. Whether something was proved true, or proved true, the underlying intent is to claim that it is true.
Related note: There is some debate/confusion about whether to use proved or proven. I think both are acceptable past participles of prove, and which you choose is pure personal preference.