Personally, I think Doc's reaction here is pretty narcistic. Although that is also human nature. Whenever someone close to us leaves on bad terms, our thoughts naturally go to "what did I do?".
I think Doc is overthinking things here. I am sure the stuff he talked about played a role. I am sure the trade rumors did, as well as his diminished role on the team. Ultimately though, I think this was a life decision made by a guy who can see the end.
I think Ray wanted to find his final place to settle. This is his last stop, and I think Miami is where he wants to be. It was much less a basketball decision, than it was a decision about his life and family.