Look also at the disease vector. Plague is endemic in the marmot population of central Asia. In the 1200s the Mongols were on the move, the Silk Road got disrupted, and people travelled heavily in marmot territory (note that the plague is now endemic in prairie dog populations in our own Southwest).
Caravans and merchant ships took plague (in rats) to port cities all over Europe. The paths have been tracked. Animals were constantly close to people, and people had poor hygiene. Fleas got around. Rats were one way, but you didn't need rats. Fleas can travel on horses and in clothing.
Plague is very well studied -- the Black Death was a huge historical phenomenon.
This new theory seems to imply that travelers from Darkest Africa were coming to Europe in 1348. Pretty sure there is no evidence for this. We know where the reservoir for Ebola is -- basically Zaire and neighboring countries. That was a bit "out of the way" at the time. By contrast, we know that the Silk Road was heavily traveled, and we know it veered into marmot territory.
I don't see this theory having anything to back it up.
Anthrax has been found in parts London where cattle was kept at the time of one of the outbreaks. Can’t remember which one. That being said, I am somewhat dubious of these theories but some experts studying the science believe otherwise. I don’t think the possibility can be so quickly dismissed.