Trial and error existed before science was a thing, even if medieval academics were idiots who thought seniority was more important than observations and the reasoning used to "explain" things was often as dumb as the reasoning in the OP.

It's how garlic and salt got a reputation of warding off evil spirits because food rotting seemed like it was caused by ghosts to people who had no idea microbes existed, and salt and garlic had anti-microbial properties, which reduced or slowed the occurrence of rot and/or mold.

Of course, from there it got taken to ridiculous levels, like people thinking a ring of salt protects them from non-existent beings or garlic frightens off other non-existent beings. But it all started from noticing that meat lasted longer for those with good access to salt (or something along those lines).