I think this a bit of a gross move on Bilic's part. He's the one saying Payet doesn't want to play, but it's a belittling move to hang Payet out to dry in front of the press like that. I also can't imagine this will encourage him to improve his form.
Don't get me wrong, it seems like Payet has wanted to leave since the end of last season. But now he'll feel like the manager, the fans, and the media are against him. Don't see it affecting the harmony of the squad too well either. Bilic has said he isn't for sale so it seems like we'll have maybe another Berahino situation? Which has so far worked well for... no one.
Why did Bilic think this was a good idea? Couldn't he of given the usual diatribe of "he's currently a west ham player and not for sale and he's training for the next game" and leave it at that, instead of inviting the circus?
Edit: Oh apparently he's not training with the rest of the first squad. He probably would have to address it in that case.