Sure, but if you take an even mildly expansive definition of 'Roman' then Romans just straight up built the Hagia Sophia and the crusaders of the 4th crusade are even less Roman so maybe we're mostly longwindedly agreeing?
Difference of emphasis. You seem to think the "Byzantines" were in some important sense not Roman, or that there's room for argument that they weren't. I disagree. They knew themselves as Romans for the excelent reason that they were citizens of the Empire.
from the other perspective, the only ones not calling them roman are 'us' ... so there's that