I understand, but my guess is that the origin of this belief was from times when cold water would make you sick because it was likely to be contaminated. Given

I understand, but my guess is that the origin of this belief was from times when cold water would make you sick because it was likely to be contaminated. Given that, it's not irrational at all. If you believe something that increases your survival but you believe it for the wrong reason, it still increases your survival.