It’s level 3 on pg’s hierarchy of disagreement - the whole concept of which I find interesting: http://www.paulgraham.com/disagree.html
If you want to have a productive argument (as opposed to just being an asshole screaming at passerby) you need to convince people that you are worth engaging.
This means showing good faith and not being overly dismissive (i.e. tone).
If you're talking about convincing people, proper tone is a prerequisite to conveying information.
For most communication, tone starts out being infinitely more important that anything you're saying. Once you reach an inflection point, tone is sufficient and correctness can take priority. The inflection point varies based on your audience.
If my tone is such that many people engage constructively, then it may well be useful whether or not I'm correct, as either people learn from my contribution or people (including me) learn from corrections to my contribution.
It's more than a little context dependent and YMMV, of course.