Is there something forbidding this kind of behavior in his (or players' in general) contracts? Otherwise, it's none of their business what he does in his off-hours, if it's legal, right? What if he had been driving all night to visit his sick grandmother and then showed up just before the game?
I think you understand the difference between the team hearing CJ Abrams was up tending to a sick family and what in fact was the reality leading up to this demotion.
If CJ Abrams was hitting the ball all over the park and playing good defense, they'd probably have benched him for a game or two, but they'd move on. They didn't send Abrams down for one problem. This had to have been after a run of issues fans aren't privy to knowing.
I have no reason as a fan to think his behavior is part of his recent struggles, but I also have no reason not to think him being out until 8:00 am in the morning before an afternoon game isn't at least part of why he went 0-3 and helped the Nats extend a losing streak.