no no, it can totally work if you use an OR.
You can play, say CAR, which is a valid hard mode move for one side, OR you can play something that's a valid hard mode move like DOE for the other side. As long as your word is a hard mode move for one side or the other, it's allowed.
I've been playing this way and it's definitely possible to win. I've only lost a handful of times, in fact.