Well DUH! I don't think people, at any time, ever thought that cold temperature itself could make you sick as if it was a bacteria. It was always understood as a cause and effect type thing. Sometimes we take too much of a revisionist view of the past - that everything thought or done in past times must be wrong or dumb.
I always though that our core body temperature being lowered probably lowered our immune system, but didn't know how. He discusses this at 1:28 to 1:52.