Latin was, for several centuries after the foundation of Constantinople, the administrative language of the Roman Empire (both East and West). It is true that modern Greek owes (some of) its origins to classical Greek, in the same way that French, Catalan, Spanish, Portuguese and Italian have their roots in Latin; but, unlike classical Greek, Latin is actually still a spoken language, therefore serviceable for modern -day administrative idiom.
It is also true that the Bulgars speak a variant of the Slavonic language, but the Romanians have a language which is closer to Latin, as their very name suggests, than any west European language.
As to the argument from religion, the Germans might well protest at their language not being recognised as an internal language of the Commission on the grounds that German was the language of the Reformation. But then as we all learnt from our great uncles, God is an Englishman!
JOHN F CRAWFORD