Whenever a Έλληνας (Hellonas - I think) uses the term Greek or other Anglicised word then we (whoever we are) could sue right back!
Modern Greek is just as close to old or classical Greek (and that's a PHD discussion) as modern English to German or Dutch (and that's another diss.) Throw in borrow words, pidgins, creoles and that and it gets complicated very quickly.
I won't deny that say, ichthphi ... (OK I searched, I can say it but not spell it) ... Ichthyophthirius is Greek derived and possibly one of the finest tongue-twisters known to man, casually thrashing physalis and the like. Closer to home, politics and other words derived from Greek (mostly an old version) are more familiar examples.
Language is always a tricksy thing. When I was a child I studied Latin, French, German and English. All to a greater or lesser extent. Now I'm 50+, I actually understand some of the interplay between them. That doesn't mean that I can speak German (bit sad - I lived in West Germany for some years) but I do understand why Wegburg and Waybury look suspiciously similar.
Nearly all languages these days are an amalgam. English is famous for "stealing" words but it isn't alone, by any means. Welsh borrows mercilessly from English for obvious reasons. However, what all languages have is some sort of cultural independence, be it accent, words, diacritics, alphabet, pronunciation or even sheer bloody mindedness.