I wish EY was around to give a better answer, but two things:

First, like you said, it's been done since the dawn of time, so that by 750 years ago, to give the date you also used, they probably got most of the kinks out of the system. You know how, in the Old Testament, Moses(?) forbids pork, and, by the Roman era (or, the dawn of Christianity) they've figured out how to make it safe, so it's unbanned in the New Testament? I think it's more in line with that, than the handwashing.

Another thing to consider is that, like you said, handwashing is a recent discovery. People were getting all kinds of food/beverage borne ailments well into the 20th century because of improper sanitation. Salmonella, trichinosis, etc. Hell, there wasn't even regulation of "pure" food and drugs until Teddy Roosevelt was President. It's likely that there were lots of bad beer cases that were never properly diagnosed.

It's probably a combination of both, so, just like they figured out how to cure pork, generally, and a bad butcher or cook could spoil it locally, same with booze generally and specific brewers locally.

But all the knowledge in the world ain't gonna help when a butcher, or a brewer, don't give even the two shits to wash his hands before leaving the facilities.