I've heard this reasoning (that 80 col terms are directly due to the 80 cols on a punched card), but never any proof.

Frankly, it sounds like numerology, to me.

"Hey! Both these numbers are 80, and they describe closely related dimensions. No way that's a coincidence! The newer one must have been specifically chosen to match the older one."

While it could of course be true, until I see reasonable proof, I'm going to assume that both values were the outcome of fitting a data representation (holes or characters) into a size that was effectively fixed for other reasons (standard card size, commonly available paper and CRT widths).

Especially since IBM later put out 96 column cards.