The argument that some of you are making is wrapped entirely in ceremony and traditional lore.
This is the only case in history where anyone will argue that a successor state of an empire with totally different cultural makeup, geographical situation, and governmental structure is in fact the same state as the one it succeeds. I mean, this is particularly glaring as the name "Rome" is not the name of a federation, nor is it the name of a nation. It is the name of one city.
Think of Rome as a great tree. The tree's roots spread throughout its vicinity. Over time, the roots take such hold that they spawn new trees with roots of their own.
A great earthquake and fire eventually cripple the great tree, and sever it from its offspring. All ties but an external resemblance between the younger tree and its parent cease to be. What exists now is a new tree with its own network of roots, and its own area of influence. Is this the same tree, in fact, as the other tree? I did not ask if it is still in fact part of the same federation of roots and saplings, I asked is it the same tree as its parent?
My answer would be no. This young tree is a new thing, disconnected from its parent, and though its bark and leaves resemble the parent, their configuration and span will never be the same as the parent's. The roots with which this young tree mingle are different from the ones that surrounded its parent. Resemblance is not only skin deep.
My friends, the fanciful augmentation of the Byzantine civilization with the trappings of another city and selected parts of its' tradition are only skin deep.