They don't have to send someone home, they just can't use register all of the players they currently have. It's quite possible a guy like Hutson or Howard accepted their invite knowing as much but want to be there for the experience nonetheless.
I was actually trying to look up the rules about this to see if there was anything in the rules about keeping players around who aren't technically registered for the team. I couldn't find anything, and you beat me to it.
Since I couldn't find anything that must mean there aren't actually any rules against it. Only other time I've known about the rules about it are in another sport. At the Rugby World Cup, if a player gets injured he has to be sent home and isn't allowed to be "with the team." I'm not sure if I ever knew the specifics on what "with the team" means in the first place, but when I've followed the RWC, teams will send injured players home. I suppose they're free to return to the host country at their own expense, but none of them do. The RWC does allow for injury replacements during the tournament, but they have to be brought into the host country as needed instead of being allowed to be "with the team" (whatever that really means). Of course, matches at that tournament are generally 5-7 days apart, so they can get away with it. Wouldn't really work at a hockey tournament where the games are every other day or another game the day right after the other.