Oh gosh what an awful situation. Good on you for your calm, intelligent responses. You have a good case here—that there is no case to be had. This situation seems akin to the classic police tactic of just "wanting to chat with you, ask you some question, no pressure" and then incriminating statements can be extracted and interpreted from any statement you make. No doubt that's what would have happened if you'd gone in for the meeting.
It sucks that these departments feel the need to almost CREATE a violation when a single person files an unsupported, hollow claim of a violation. They disguise this as just a matter of following due process to ensure safety or something.
