I don't see how you can read the draft reg and still say that. Article 4(1)(c) of the Basic Regulation covers a "non EASA registered aircraft inside the EU if [the operator] happens to be a resident of the EU". Article 1 of the FCL cover regulation brings the pilots of these aircraft into the scope of Part-FCL. Article 3 of the FCL cover regulation says that these pilots must be qualified in accordance with Part-FCL, in other words that they must have an EASA licence or validation.
Because that is exactly what the Basic Regulations say. You cannot compartmentalise regulations or sections of regulations. You have to have regard to the totality including Article 7 of the basic regulation and indeed to the treaty obligations of the member states, one of which is their obligations under ICAO. There is certainly a presumption in English law when interpreting statutes that the state does not intend to legislate contrary to its international obligations. So, it is unlikely that EASA intends to cut across international obligations in the way you suggest.
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, but that is clearly not the intention of the Regulations, nor its effect. I recall a friend who flew for Cathay having to have HK ATPL because the aircraft were Hong Kong registered; likewise if you fly for BA, Air France Air India etc. That is logical, but I don't believe for one second that EASA intends that every pilot crossing its borders but working for a foreign carrier with foreign registered aircraft needs an EASA ATPL.