As far as I know, the status of whether the privately-operated terminals at JFK allow personal photography is a little up in the air. PAPD has a history of saying that photography isn't allowed, but I haven't seen any rules posted or laws that confirm this. However, the most they could do would be to ask you to leave. I'm not sure how kicking someone out of the terminal would interact with their conditions of carriage; I assume they'd have to refund your money. IANAL, though.
(See the
thread in which FTer marklyon was nearly arrested by PAPD for something similar at another JFK terminal.)
UA also apparently has a no-photography policy, but I can't see how they'd legally enforce it, especially at places like check-in desks where there would be no expectation of privacy, and given that LEOs aren't charged with enforcing corporate policies.
Agreed that once they played the 9/11 card, there was no possibility of a rational discussion with them. The employees, even if they were covered by UA policy/terminal-operator policy/local laws against photography at JFK, clearly were muddling their arguments.