Correct.
There is one exception. The FAA allows you to fly an N-reg on a foreign license, but only in the airspace of the country that issued that foreign license. Note "issued" not "issued or rendered valid", and the FAA doesn't recognize EASA-land as such ATM. So if your EASA license happened to be issued by the UK authorities, then the FAA allows you to fly the N-reg on that license, but only within UK airspace. And there are a few other limitations that apply.