First of all, Reggie maintains to this day that Ward put those words in his mouth, that he was misquoted. Whether this is this case or not, I don't think Reggie thought of it as starting trouble with Munson or the team when he gave the interview. I don't think he thought about anyone else at all, which was often the case.
That's not to say that he meant them disrespect, but Reggie was always a cocky, big-mouthed dude. He has a big and fragile ego, and was genuinely hurt and surprised when the clubhouse responded to the Sport article so coldly; he was too self-centered to see how his comments had hurt them.
I think "The Bronx is Burning" does a decent job of showing these conflicts and the emotions behind them. I was a grade-schooler in Jersey when the Yanks won it all in 77 and 78, and I never get tired of this story. For those interested in learning more, I recommend Roger Kahn's book "October Men".