It's nothing to do with the residency of the pilot. It is the operator of the aircraft that matters. If they can legitimately say that the operator is based in the US, then no need for an EASA licence. If the operator is Europe based then ORO.FC.100 (b) applies which says that all crew must have a licence issued under Part-FCL. That doesn't mean they don't also have to have the licence required by the state where the aircraft is registered.
I hope that helps!