Just getting along with people is pretty reductionist on that idea I agree. It's a fantastic book and I agree with you on every part other than that bit of explanation. I think a better way to phrase it might be to find a way to say things in ways that aren't offensive, which takes a long time to learn, and don't look for a fight when it isn't looking for you. You're not always going to be able to say the same thing to different people and get the same results, this is a lesson that took me a long time to learn. I would say things I didn't find offensive in the slightest, nor did I mean in any way insulting, however others would take it as a personal insult, even if it was just simply the reality of the situation.
A way to meet the second part of don't go looking for a fight is to follow advice that's actually a rule here and assume the best possible interpretation of what's being said.
I really love this recommendation.