Considering the fact that poison can shut down the mind, the type matchup should be the other way round.
One theory is because poison was related to fatal diseases, and psychic was related to willpower. Apparently people have a much higher chance to survive diseases if they have the will to live.
The answer is basically what you said but in reverse.
Psychic is super effective on poison because psychic powers remove toxins, not toxins shutting down the mind (Although that is a good point).
So basically what you said in reverse.