Is it me or does this solution rely on the belief in a certain order to the random picking of prisoners? If the counter switches to an off state 44 times, that

Is it me or does this solution rely on the belief in a certain order to the random picking of prisoners? If the counter switches to an off state 44 times, that doesn't tell him that all 22 other prisoners gave toured through the room. A guard (random algorithm) could have just selected the same two prisoners -- the counter and another guy -- 22 times. Am I missing something?