They weren't actually all that much smarter in those days. They used to kill cats because they thought cats were a bad omen… allowing the rats to spread out even farther.

Also, they didn't wash.

Ironically, the reason people avoided bathing was because they thought it made them more susceptible to disease. The predominant theory of disease (throughout the Old World, and not just in Europe) is that disease was caused by miasma, or foul-smelling air, entering the body. By regularly bathing and thus keeping your body's pores unobstructed, it was thought that you were just giving the miasma more ways into your body. This is how you end up with a Europe where laundry is an important chore and where people like Queen Isabella of Spain thought bathing once a year was commendable.

Miasma theory is also why the plague doctor garb has that distinctive beak. Sweet-smelling aromatics, which were thought to counter the effects of miasma, would be stuffed into the beak, making it a kind of medieval gas mask.