The problem with the "aviation system" was that ZNY went ATC Zero due to a "staffing trigger" caused when controllers tested positive for COVID-19 and had to be pulled from the facility - Not enough controllers to keep it going safely, so they ground-stopped everyone both in and out and turned around inbound flights. They got more controllers in about a half an hour and reopened (and many of the flights that had been turned back were allowed to turn inbound again). The facility went ATC Zero again overnight when they closed to clean and disinfect, and is now open again but on ATC Alert status.
So yeah, from the Port Director's point of view, THEY did not discontinue flights due to the Coronavirus - The FAA did, due to a "problem with the aviation system" - ZNY closing due to - wait for it - Coronavirus.
Good ol' PR doublespeak. But chances are the CBP guy doesn't even know what ZNY is. He knows about JFK, LGA, and possibly N90, none of which were even closed. That's why it's "the aviation system" - He's clueless as to the workings of things once off the ground.