There's no reason why you have to be "consistent" from street to street. What you're trying to do in poker is pick the decision on each street that maximizes your EV. These are correlated, but different, ideas.

I don't think Our House was anywhere near 100% sure he had the best hand at the time he raised. In fact, I'll wager that he was less than 50% sure. But there was enough of a chance, compared to the pot size, for him to represent the best hand and raise. On the turn it's now heads up and checked to him. There are several great reasons to check behind as opposed to betting given that he's probably up against a better hand.