Sam Mitchell certainly didn't allow Bargnani to not rebound or play defense, no matter what management might have said. And he was his coach the first 2.5 years. As for Triano, I know a lot of fans around here don't like him, but he's smart enough to know you're not going to win much without your big man doing the dirty work. Besides, I've seen Triano yell at Bargnani for not doing that exact thing.
And I don't think management is going to micromanage things from behind closed doors. That simply doesn't make any basketball sense. Why would they do that?
I also think that you're forgiving the player far too much. If I'm Bargnani, and management tells me that I don't have to rebound or play defense, I'm smart enough to know you aren't going to win that way. This isn't Nazi soldiers following orders, here. If Bargnani doesn't have a high enough basketball IQ to realize that's a horrible way for a big man to play, then the fault lies with him, and he should be shipped off immediately.
For more reading on Bargnani, I just posted this on him...