My use of the term 'invasive' was used in reference to very specific geographic areas wildwood. The North American Grey Squirrel was first classified in the States of Carolina, hence it species Sciurus carolinensis. As you correctly point out, the species does inhabit several areas of the North American continent. However, there are/were areas where it had not been priviously reported, especially in the Pacific Northwest. (Here in our part of the western U.S., the squirrel is known euphemistically as the Pine Squirrel.) In those areas, the smaller North American Red Squirrel (Tamiasciurus hudsonicus), although gregarious and somewhat aggressive towards the Gray, was found, over a period of time, to be supplanted by the Gray once the Grays had been introduced (by various means). The primary factor attributing to this phenomena appears to be the more numerous offspring of the Gray. The study surprised the researchers in that the Red's population dwindled with no signs of interbreeding in very similar species...
Thanks, for your observations!