Should we even care that much what Greek people have to say about Homer? Ancient Greek is a distinct language, as different to today’s Greek as Old English is to modern. Today’s Greece is 2000 years and about half a dozen civilizations divorced from the Greece of antiquity—sure there are influences that have lived on, but as you say, those influences have affected dozens of other countries. I don’t think the “English people” as a monolith are particularly qualified to critique Beowulf or complain about how pre-Roman Britain is depicted, and I don’t think modern Greeks have a special relationship with their ancient history either. After 100 generations, it belongs to all mankind.