Even James Blish, who used the "Earth colony" retcon to explain "Miri" away, doesn't use it in his "Omega Glory" adaptation, in part because there's no way to reconcile it with the age and history of the Omegans.
There was some debate as to exactly how far in the future TOS took place, until TNG put all that to rest...
So I have no idea where you got this notion of a deleted scene from, unless it's from your own imagination.
Please don't ever accuse me of lying ever again. You want to know where I got that? Right
HERE, that's where. If you have a problem, go talk to whoever wrote the Memory Alpha article, capisco?
And besides, can you come up with ANY other explanation as to how Omega IV could have evolved EXACT COPIES of the Constitution, and the US flag, and the terms 'Yankees' and 'Communists'? I highly doubt it. There can be no other explanation - these people are humans. It MUST be true. Now, exactly how humans got from Earth to Omega IV, is of course highly variable. But that must, by definition, have happened.