From what I gather, the Rockets believed they had an understanding with Parsons that they'd let him out of his contract a year earlier so that he could get more money faster on the condition that he'd reup with them. Parsons, feeling slighted that Houston didn't consider him a third star, promptly signed a max offer sheet with Dallas. That essentially forced Houston to pick between the chance at Bosh or keeping Parsons, when they would have been able to keep both. Of course, they ended up with neither.
The fear is that Leonard would do something similar to what Parsons did if he doesn't get a max extension. From a standpoint of securing the most cash he can, it makes sense for Kawhi to sign with the Spurs next summer for a five-year max deal. That would help both sides. But if he feels disrespected by the Spurs prioritizing future cap space over allaying Leonard's concern over a new deal, Kawhi may go for a short-term deal with a new team. The Spurs could and would match (provided the other team didn't have a of a S&T package to offer), but it would both put a constraint on how long they had cap space next summer and make 2017 a year where they have to appease Leonard in order to convince him to stay. The Spurs could end up in a situation where Kawhi walks in 2017 because the team isn't compe ive, where the main reason why the team wasn't compe ive is because Leonard took his money a few months too early.
The obstacle/thing to watch here is not the money; the Spurs will give Kawhi his. It's all about how Leonard handles these negotiations. In my opinion, he simply isn't good enough for the Spurs to kowtow for. If he plays this like we expect Spurs to do (have a team-first approach even though he's going to still get a max deal), then things will be fine for everyone. However, if he ends up being a diva about this like Parsons did, it's possible that it won't really matter if he walks or not.