I've never taken graph theory, so I'm not sure what 'simply connected' means, but can't that algorithm get you stuck in a loop if you start with one on your left?
I really think there was more to it. Something was not correctly said or understood.
Simply connected as in there are no "floating" walls that aren't connected to anything else, because then you could get stuck in a loop with the left hand solving technique. When I was in college we made sure the mazes we were working on were simple by starting with a graph where no nodes were connected and adding edges one at a time until the entire graph was connected.