>but does this "myth" have any merit?

In the middle ages people had a good understanding of basic hygiene, in short immersing yourself in water (warm if you can afford it) is good. The Romans had bath after all, it's nothing groundbreaking. And yes there were many bathhouses in medieval European cities which served both as bath houses and brothels.

The "dirty era" is actually the modern period (16th-18th centuries). Because bath were seen as dangerous: doctors thought that pores would open in the bath and let enter all the diseases. That's where you see stories of "a man proud of never having taken a bath in his life" and actual doctor saying that washing anything more than the hands and face is unhealthy. There's a reason why everybody stank at Louis XIV's court.