Law Lord, yes you could do that (absent a fully accounted head count on the B to C segment). If you get off at B to stretch your legs and get back on the plane, you just show your boarding pass at the gate; there is no transaction (e.g., another boarding pass or another portion torn off or something like that).
The problem is that a situation like that (as opposed to a change of planes at B) is quite rare. Plus, your choice of schedule is greatly reduced. And, finally, you only get 1/2 of the fare savings of flying to C instead of B.