No no NO!! This is a myth!!! Psilocybin in its pure form sure. But physical magic mushrooms absolutely DO vary in potency. My partner had what he thought was a low dose of mushrooms, because in the past he'd had a similar sized mushroom in the past. But this mushroom was WAYYYY stronger and he was catapulted into a catastrophically bad trip that resulted in him hallucinating that his best friend was trying to murder him, and he shot them believing it was self defence. This was partly due to the fact that you do NOT know how strong your magic mushroom is. He had a small handful in the past and it caused nothing but pleasant sensations and rainbows. Then he had another small handful another day from a different dealer, and it led to complete and utter psychosis that not only led to someone's tragic death, but also to permanent mental health effects that last to this day almost 5 years later!!
Yes I think preexisting mental illness definitely played a part. But thinking magic mushrooms don't vary in potency is a recipe for danger.