Interesting topic. Well, they are actually right for using Latin for the Byzantines since it was the official language of the empire for many centuries. However Latin coexisted with Greek there and a change to medieval Greek may be more proper since the majority of the Eastern Romans were speaking Greek and other dialects of the Hellenic language. I would say it’s a minor issue to fix but still worth mentioning.
Ohh By the way Byzantines can not be only Greeks since they were a multicultural empire, Assyrians, Greeks, Latins, South Slavs, Armenians, Jews, Paphlagonians, Phrygians, Egyptians etc
Greeks were not called Byzantines back then neither Hellenes. The name of a medieval Greek was ‘‘Romios’’ and it actually means Roman. Since 1821 Greeks were calling each other like this (and their country Rhomanea, that means ‘‘the state of Romans’’) but then they made a swift focusing more on the ancient Greek heritage rather than their Roman past, changing their national name to Hellinas(Greek) instead of Romios(Roman).