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FCC isn't involved in this? I mean.. could a private party set up a fake cell phone tower legally?

Just asking because I don't know.

No. They need probably need to get a "Special Temporary License" like the Burning Man cellular folks do, http://en.wikipedia.org/wiki/OpenBTS#Burning_Man

or be operating in a time of national emergency in an emergency response function.

Yes, not without permission

So the question is do they have it?

Yes,they do.