A couple of years ago, a user by the name of @goferet was sending regular rape and death threats to women. I saved links to 8 of the rape threats and 2 of the death threats, and contacted Twitter support.
They responded that his actions did not violate their terms of service. I pointed them directly to the terms of service page, and the specific mention of threats.
They didn't see a problem with what he was saying. Specifically things like he was planning to climb in their windows at night and rape them, some of them past rape victims who were campaigning for better investigations and fairer treatment of victims.
I thought maybe it was just the one idiot in support I was getting, but even the @support account didn't think anything of it.
What eventually did stop him making the threats was that I contacted people that he was associated with on Twitter and suggested they read his feed directly, so they could see what he was doing in his mentions, outside of the regular feed they saw. There was some disgust, and one person who knew him got him to finally shut his mouth.
Obviously there was an element that could have been "Leave it to the police", especially when some of the people he was attacking lived in the same city. But since Twitter was ignoring their *own* policies to let him threaten other users it was pretty vile on their parts.