Who said anything about "illegal" basing? If airplanes are based illegally, then I'm sure the appropriate authorities will take care of the situation!
I see airplanes registered in various EU countries operating in the US all the time, and have heard no objection to it. I have NOT, however, seen any "EU registered" airplanes. Is there such a thing as "EU Registry"? If so, what is the EU registration prefix?
It is VERY clear that the main objection to the "Norwegian" long-haul proposal is that it CLEARLY uses a flag of convenience in an attempt to cut costs below the norm, avoid regulation, and engage in cabotage. If that is NOT the case, then the operator would simply register the airplanes and base the crews where they do, in fact, operate. If operating Oslo to JFK, then either Norwegian or US registry and basing would be perfectly acceptable.