Not actually true. The colonies could have received the things they wanted had they actually attempted to fight for them (and by 'things they wanted', I mean the things we wrote about England (and specifically a king with little political power at that time (it was all parliament's by that point)) not giving us).
The American Revolutionary War was started because of political activism. They saw a chance to start a new country in whatever manner they pleased, and leapt at the opportunity. Even just a little effort put to really trying to get a voice in parliament would have worked fine, but instead we went and write the bloody Declaration in an attempt to rally support of other nations not really pleased with England (I'm looking at you France), and filled it with rhetoric, half-truths, and blatant lies. Okay, maybe not blatant, but they're there.
Really amazing that a war is mistaught to most American students. Okay, it isn't that amazing, I mean, you're going to teach your country's history in the most favorable light possible, but, still...