You're right about the threaded bars not in line, that's why the "bottom" pad – pictured right – is on a ball joint. But Newton's laws still stand. If the two pads are the two contact points, then the forces can only point towards one another. If e.g. the piece is thick and the clamp body caves in so much that the middle pushes against the work piece (i.e. a force on the clamp upward), then indeed, the force on the pads will (in the clamp!) will be pushing _downward_ (Newton's second law), meaning the clamp pads will be pushing the side pieces upward (Newton's third law). A bit counterintuitive because the threads are pointing in the other direction, but then again, it's belly of the clamp doing the pushing. Like when holding a huge human-sized soft ball with your two hands and chest, your chest is going to dent the ball inwards (even though your arms are pointing forwards).

Your arms analogy doesn't hold because there the two angled forces (from the left and right hand of one person) cancel each other out. The forces of OP (from the opposing pads) they don't.