I'm not going to speculate what's going on in his personal life.
However that statement to me reads the team told Miller to take time off. Something has been off with JT this entire season. He's been mopey, I noticed it when the press asked him about Lekkerimäki's first goal, his response was "I passed him the puck, he shot it, and it went in". That's not a response you expect from one of your better players. Even the benching and Tocc's comments post game, something seemed off.
I don't think it's out of question that something happened in the lockerroom with JT, either with a player or a member of the coaching staff, and the team felt it was best he didn't come on this road trip. Do I think Miller wants out? Hell no, but the dude is emotional, and I could see it rubbing some people the wrong way.