Proof has never been used to justify arrests, just prosecutions. Or rather it's never been a necessary bar that must be demonstrated. Warrants at least have mildly higher bars
Reasonable articulable suspicion of committing a crime is a bar. Quite low, but "suspicion of committing a crime" is not met based just on an anonymous tip, as SCOTUS said quite clearly. It is enough to investigate, not to arrest and not even to detail someone.
Agreed. I don't think the police response is inherently unwarranted (well except literally, ha ha) but the protocol surrounding how to handle the situations appears completely busted.