If your interpretation ware to be correct, then every Delta Airlines pilot or Emirates Pilot flying in to the EU would need an EASA ATPL
Neither Delta nor Emirates are "an operator established or residing in the Community". They fall under Article 4(1)(
d) of the Basic Regulation. Article 7 of the BR does not apply to them, and Article 1 of Part-FCL does not place their pilots within its scope.
The issue is about operators of foreign-registered aircraft "established or residing in the Community", covered by Article 4(1)(
c). The Basic Regulation is structured with a clear difference between resident and non-resident operators.
As you yourself pointed out in post #19, the CC allows a state to reject foreign licences issued to its own nationals. There is, without doubt, a difference between residence and nationality, but I would be rather surprised if EASA and the EC had not sought a legal opinion on the interaction of the Basic Regulation with the CC.