That actually makes a lot of sense and means it was a coincidence that the 2 and 3 door cases needed 2 and 3 levers (accepting the 0,0,0 as a starting state - it can actually be considered another lever).

The four lever counter example (0001, 0010, 0011, 0100) - door 0 is never touched by any of these is clear. It was just that 2^(x-1) covered the respective space in the 2 and 3 lever cases, heh. Thanks!