I think the people who had been living in the imperial capital - in the Eastern Empire - for over a century would have been surprised to hear that they weren't part of the 'actual empire'. Even then, Greece had been part of the empire longer than most of the western provinces - longer than any of them, in fact, save Italy, Sicily, Spain and parts of North Africa. If Gaul had a claim to be the Roman heartland, Macedonia had a better one, and that called itself 'Roman' until 1392.