I'm starting to think the Spurs believe Kawhi has a chronic injury, and it's Leonard himself who thinks he's healthier than he is. That seems like bizarro-world , but think about it: The Spurs scout Kawhi and know he has a persistent quad issue, but they draft him anyway because they think they can manage it. It flares up a couple of times, but for the most part, it's fine for the first six years. Then this summer it comes back and doesn't go away. The team eventually (rather quickly) concludes that this is just Leonard's life now. He's going to have to deal with pain and may not have the same athletic ceiling. But with enough precautions, he can still have a career, maybe even a HoF-level career from here on out. So coming to the conclusion that he'll never be the same again, they "clear" him to come back as the player they feel he is just going to be from now on.
Leonard, on the verge of a supermax, gets this prognosis and freaks out. He thinks he's just hurt, and if he can just get enough time to heal and rehab, he'll be fine. But time goes on, it doesn't get better. He tries to play through it but hates how he looks on the court. Facing real NBA mortality a decade too soon, he bolts town and tries to find someone who can get him back to who he used to be. Multiple specialists tell him that the Spurs weren't wrong, but eventually some or one of them comes up with a plan. So Leonard has been trying to do that, but as time goes on and nothing works (or as Danny put it, Kawhi has "setbacks"), his at ude becomes more and more toxic and withdrawn. It certainly doesn't he could feel/have been led to feel that this whole diagnosis is a ploy to get Kawhi on the cheap (since a permanently hobbled Leonard is not a supermax guy).
So in this case, a lot of Pop's words feel different. A lot of the sickness and disgust he's shown comes from witnessing his star player spiral. The "player-only" meeting was so tense because Kawhi returning as is is pretty much admitting to himself that the team is right about his future, which he won't accept. Tony saying his injury was "100 times worse", is an attempt at consolation and hope, not a diss. The team wanting to move on with their season was an attempt to give Kawhi space and end would likely be grueling and ineffective rehab attempts. Danny's remarks are him truthfully reporting as much as he can without getting into the nature of Kawhi's injury (if he even knows). Even this makes a different level of sense in this scenario: