Matta,
It would depend on what parish you go to. Even a good number of Church musicians are not experts in Byzantine music. Some Americans (like, in my opinion, the Boston Byzantine Choir who has several recordings) sound "western", probably because of intonation, but also stylistically. I'd imagine said choir has had a lot of influence on the parish profiled in the video clip. Other Americans sound just as good as the best Greek musicians (and they're generally Greek-Americans or even immigrant Greeks, like the Romeiko ensemble).
However, information on the intonations are
available [
stanthonysmonastery.org], and in my parish we use similar intonation. Personally, I get all my intonations from my collection of Athonite or other Greek Chant that I've built up over several years.