This is about the Byzantium section, not the whole article, if you can get your mind around that idea, we are making progress. Again I repeat
No one is claiming: 
Byzantiums invented the symbol.
Byzantiums are the only ones to use the symbol.
Mehmet II and the Ottomans definately copied the flag.

So there is no need to drown the small section in repeated attempts to show that a turk at some point passed through a nation that had used the symbol at some point as a hopeless counter.

What is being claimed:

The flag of Byzantium, crescent moon and star was flying over Byzantium when as the Turks arrived to lay siege.
Byzantium was the first state to use the symbols as national state symbols.

The fact that symbol is old has nothing to do with the Byzantium theory. It is about how the Turks came to adopt the symbol, not who invented it.  It is already stated  above (please read this carefully, i will repeat) It is already stated that the symbol has ancient roots above the section on Byzantium.  What this article is about is not how the Byzantiums got the symbol unfortunately for your nationalism, but how the Byzantiums used this symbol and how it is highly plausible as THE ONLY STATE TO FIRST USE THE SYMBOLS AS NATIONAL SYMBOLS, the Turks borrowed the symbols. Whether the Turks traveled through Places Greeks also went through has no bearing as this section is clearly about how when Istanbul was sieged, the only side using the symbols were the Byzantiums.  This however is obviously criptic to you and I am sure you will repeat your line about how Turks traveled through Babylon as some bizarre hope that it is relevant under this specific Byzantium section. The board of mediation will have to look at this I am afraid.