Actually, my reasoning is that the Byzantine Empire was in Greece until it died, so the Greeks' origins are of there. Not the Germans, they never had Greece. Not the Russians, they didn't either. Not the Ottomans because the Greeks weren't assimilated into Islam before the Ottomans fell.
And no, I was talking about the time between the first successful siege of Constantinople (by the Venetians) up until the second (by the Ottomans). As they were headed downhill ever since that Venetian capture of Constantinople. The Byzantine Empire has very Roman roots. The H.R.E, though, does not, and they don't count for any period of the Roman Empire, they were never Roman to start with.
Also, the H.R.E. did not evolve into the German Empire. It was abolished by the Austrian Empire when Napoleon conquered it. It was Prussia that evolved into the German Empire.