If doership is an illusion, then who is 'doing' the belief in that illusion? The same could be asked about any characteristic of the way that things seem to be. Hence no error can be involved in the distinction between illusion and reality, in fact there can be no such distinction, or better, no common plane in which both could be compared or put side by side. You can distinguish dreaming from waking, but you cannot do so from within the dream, but waking up within the dream can take place.