Again, you're falsely assuming it's proven that Harry and Cyrano somehow weren't Federation citizens. There is no reason to assume that, except that you don't want them to be Federation citizens because it would prove your assumption wrong. It's completely circular reasoning.
I'm not assuming whether they are citizens either way. You are assuming they ARE citizens. I am saying they obviously deal with non-feds every day, by the very nature of their business. Harry Mudd was a criminal smuggler, he's obviously in league with plenty of shady types. Cyrano is a con man, same thing. They would need money to deal with these folks.
It makes just as much sense as the fact that so many familiar cities, nations, societies, and pieces of cultural heritage survive intact after WWIII despite what Riker claimed in FC. Maybe Riker just exaggerated. Again, one should go with the preponderance of evidence. You can't just ignore a whole pile of evidence in favor of one outlying data point that contradicts all the rest.
Now riker exaggerated. who exactly is twisting the facts to fit their view? lol
Not the same thing at all. It's not like Riker said the cities were completely OBLITERATED with NOTHING left. The important parts were destroyed. Some monuments survived, some art survived, etc. A lot of it would likely be rebuilt. Not unrealistic at all.
Cell phone companies and other major corporations surviving in a world where the economy and most governments are non existent for 30+ years? That's pretty ridiculous.
Just off the top of my head, I can recall references to Paris, Leningrad, and Cambridge University as well (regarding Picard, Chekov, and Data, respectively).
In general, I'm leery of applying TNG assumptions to TOS . . . or the new movie. The way I see it, the new movie was primarily based on classic STAR TREK, as opposed to the later spin-offs, so I'm not really sure why we're talking about TNG-era concepts at all.
Those references don't really say much though. The cities may exist in the 23rd and 24th century again, but from what riker says, they were in shambles at one point. They must have been rebuilt. Now, the non major cities, and who is to say what that is, might never have been seriously damaged.
As far as tng-era concepts... We are talking about star trek canon. This is pre TOS history according to the canon. World war III had serious effects, and it seems largely ignored in nutrek. It would appear that there WAS no world war 3 at all if these present day corporations are still fine and dandy in the 23rd century. If it had been a hard reboot, it wouldn't matter. But they decided to connect Nutrek to the old universe. they can't have it both ways. (well, obviously they can, and they did, but i'm still gonna call B.S. when i see it

)
I wish it was a hard reboot, but they decided to take on all the historical baggage of pre-kirk. But they largely ignored it.