Fringe kook theory of the week. Yersinia pestis has been clearly identified as the infectious agent from european plague pits.
The rats not dying en masse doesn't really impress me.
Animals are often immune from human diseases, and vice versa.
Very bad viral diseases like HIV/AIDS, and Herpes S (Simian) came from animals fairly similar to us, genetically, like monkeys and gorillas.
I'm sure everyone has heard the theory of the green monkey that "someone" in Africa either ate, or had sex with.
Thus a terrible virus, HIV became so lethal to humans.