Actually "Greek Old Calendar Churches" could refer to the Greeks who went into schism from the Church of Greece over the adoption of the New Calendar. In which case, they are certainly not in communion with Rome as the objection to the New Calendar was in part that it was adopted to move the feasts of the Orthodox to coincide with those of heretics (that is papists).
The Greek Orthodox old calendar church being referred to is one that broke from the (New Calendar)Greek Orthodox over the changing of the calendar.
Thank you for the clarification on communion with Rome.
Unfortunately there seems to be alot of misinformation over just who is in communion with Rome. Add to that people not paying close attention to what I'm telling them and it's very frustrating.
Interesting definition. However, please don't use the term "papist", it is a disparaging term