>>My experience suggests that if you do that, the other party will never stop disagreeing with you no matter how far up the chain you go.

Absolutely true.

There was a MOOC about argumenting at coursera I think. The proffessor had the same viewpoint. One of the lessons was that you have to start at a common reference point and argument from there. If you and the other person have no common reference points, you will never resolve your difference of opinion ever.