Here's my take on the story ...
From what I understand (and I'm not saying this is fact, just what I was told), Kawhi got his feelings hurt because someone in the organization (not a player, not Pop) said in not-so-kind words that he was being a wimp about the injury. Kawhi wasn't that riled up about it, but was offended. Mentioned it to his Uncle, and Kawhi's group then got Kawhi really riled up about it (saying he was being disrespected, not appreciated, Spurs were too controlling, Kawhi wasn't having input on player signings, etc.) Side note: I believe that Kawhi really only cares about playing basketball, but he trusts his advisors completely, when maybe they are just looking out for their own best interest not necessarily his.
At that point, anything the Spurs did or said to Kawhi was met with resistance by the group and blown out of proportion by the media. (For example, when Tony talked about Kawhi's injury, that was actually a comment in support of Kawhi -- go watch the video again. "Worse" things were said by other players privately, but none of them were trying to slight Kawhi - they were just confused/frustrated by the lack of communication. Kawhi was just trying to rehab and had turned over most communication to his group.) Kawhi was never pissed off at any of his teammates or even really with Pop. He thought he was physically not able to play at that point, and he had become convinced that the grass was greener elsewhere. And he was right... he just won a Championship.
I think that communication could have been a lot better on both sides, and I think Kawhi could have done a lot more to improve that communication. I also think he could have played more than those 9 games, and if he really couldn't, he should have been sitting behind the bench in support of his teammates. But I'm not one of the many doctors he consulted, so what do I know?
Do I think he will stay in Toronto? Probably not. He's probably very happy there (especially right now), but again, "coming home" to California is a big appeal to him and the group.
Disclaimer: There's more to the story but this is the beginning of it, and timvp has some insight on that info that he may or may not ever share.