How about one person and a rape accusation from 20 years ago?

That's the purpose of statute of limitations.

Didn't many states eliminate or raise those for large categories of violent crimes? This means that a rape today for example could be prosecuted decades from now

A rape accusation just under the statute of limitations is going to require more than just a single accusation. Obviously physical evidence is impossible but they usually go on any information the victim shared with associates ("she told me he raped her the previous night" or there's an authenticated diary detailing the crime), the closeness of the suspect and victim (they knew eachother and likely were in close proximity), any corroborating witness testimony ("I saw him follow her home that night after the party"), and any character witnesses that may have shared similar experiences ("he was rough in bed and wouldn't take no for an answer"). It's difficult to convict on old crimes like this so a DA is going to be very selective on choosing to prosecute, they aren't going to waste their time if the accusation is paper thin or the victim is unreliable. Of course it's entirely possible everyone involved is lying but again, a careful DA is going to do their research before trying the case.

A suspect is under no obligation to prove their innocence but when it comes to circumstantial witness testimony, the suspect absolutely must do everything they can to fight the narrative.

If 10000 people witnessed a crime for which there was no physical evidence present, yeah I'd say something is very suspicious and would not convict.

If 10,000 people witnessed someone pushing someone off a rooftop, you wouldn't convict that person?