Nothing though in the document seems to affect the principle that FAA licence in N reg aircraft = perfectly legal, irrespective of residence, unless a regulation says differently, which at the moment it does not. I wonder though how many FAA IRs will be rushing to do the exams and 15 hours just in case ...
What interests me is what EASA proposes to do regarding pilots who are flying ICAO (non EASA) aircraft on ICAO licenses.
I think you're missing the bit of the cover regulation that I quoted. Article 3 requires pilots involved in the operation of aircraft that are registered in the Community (Article 4(1)(b) of the BR) or registered in a third country and ... used into, within or out of the Community by an operator established or residing in the Community (Article 4(1)(c) of the BR).
Thus if you, as an operator, are resident in the Community, you are required to have an EASA-Part-FCL licence even if you fly a foreign-registered aircraft. BillieBob has set out the (very limited) conversion and validation options.