You're contradicting yourself all over the place here.
I'll say it again: the only hard proof we're going to get is if they're cleared by the rules of the game we're playing, by staying another night in jail. So we agree on that, at least, but where we disagree is on letting them out for the day.
Talk to them. If they don't confess, which they won't, let them out to get some air and some half-decent food, and we'll lock them up again tonight.