There's a difference between figuring out "hey, sicknesses are spread by little dinky creatures too small to even see -- cleaning your hands before handling wounds kills a lot of them off, and makes it less likely that they'll get into the wound in large enough quantities to infect the patient" and figuring out that "hey, some sicknesses seem to spread easily from sick people to healthy people, regardless of the environment"
Hell, Vlad Tepes III -- the actual Vlad Dracula/Vlad the Impaler/Kaziglu Bey ("Lord Impaler" in Turkish)...whatever you prefer to call him, so long as you're clear that we're discussing the actual historical figure, not the fictional vampire -- figured the latter one out.
When he was fighting the Turks in the 1400s, he sent sick peasants with all sorts of diseases into the Turkish army's camps. If any Turks died from the same thing the plague-bearer had, that peasant got a reward...assuming he or she didn't die of it as well. (Though Dracula might have paid the reward to their families in that case. Man was real big on rewarding peasants who served him well -- the other side of his "incredibly tough on crime/disloyalty/" attitude.)