actually the 14th century had proto vaccines where they blew germs through a straw up the patients nose to get the infection over with, so little farther back, people back then had at least some idea of how microbes work
I think that was more a case of "Even a stopped clock is right twice a day." They had a lot of funky ideas about imbalanced humors and miasmas causing disease.
Of course: human intelligence seems pretty constant. But they were hampered by a lack of knowledge (and consider the ways in which the church's almost complete monopoly on literacy kept people from passing around ideas easily, and radically shorter lifespans among the lower classes kept people from freely applying their intelligence).