Yes, it's nice because you can be nice since you're clearly right, you can express your frustration and ask for their help instead of yelling at one of the two parties that is treating you like a ping pong ball.
Warning, I didn't get any answer from the legal department, suddenly the problem just went away, like magic
They don't want any bad press either and I'm sure they don't want people to suddenly realize there's a legal department and bombard them (hence, no response from them). It would have never occurred to me to think of it if my old boss hadn't mentioned it but it does make sense.