His response to ""Don't message me SO MUCH or I will BLOCK YOU", followed by a block when the messaging remained unchanged was to file a series of nuisance complaints about her and start messaging her friends and employers.
I don't think any reasonable law enforcement agency could conclude that this behaviour wasn't a problem because she hadn't asked him to stop.
There's no question that his behavior was "problematic." What is not at all clear in that scenario is whether or not it was unlawful for him to continue to communicate with her. "So much" literally means there is an acceptable amount of communications. Blocking on Facebook is a completely passive action which does not directly communicate anything. Sure you can deduce that she didn't want to hear from him again, but she should have sent an unhedged message to cease and desist further contact, THEN block him.
I don't think any reasonable law enforcement agency could conclude that this behaviour wasn't a problem because she hadn't asked him to stop.