You push people, you'll get pushed back. How else would you handle it? Other than bringing it to a supervisor, which I did.
I'm not saying what you did was "wrong." It would seem that in hindsight, you picked the "correct" choice, seeing as you got what you wanted.
Honestly, I'm not sure what I'd do in such a situation. I've dealt with a person like this at an old job. She was strangely vocal and particular with how others responded to her (tone, inflection, body language). The thing is, she would provoke aggression by way of being nit-picky and criticizing the quality of work in others. This was outside her jurisdiction so it's only appropriate that people would start to get agitated. She seemed oblivious. I found better work and left, so who knows what I would've done. Probably confront her and try to seek a compromise, of course assuming it would interfere with my quality of work and I'd actually get annoyed enough.