While Europe is obviously not a country, for EU members it is a common market. The free movement of goods and services etc. As such, from a commercial point of view it should be viewed as one "country". Since the kind of aviation we're talking about is of a commercial nature, it should be treated just like any other business.
Hence, non-EU registered operators should be allowed to operate within the EU only under the sames rules applying to an EU registered carrier operating in the visting carriers "country", be it political or commercial. So, when a G-reg aircraft is allowed to fly JFK-ORD, N-reg'd aircraft can fly LHR-MAD. Or A40 reg'd aircraft can go BRU-OSL when OO-reg'd aircraft can go BAH-DXB (or within the GCC countries in other words). Simple, really.