1) crew checks systems prior entry into ETOPS area as per FAA
2) check is not ok so cannot enter said area
3) only way to get out of NATS OTS is declaring emergency (as noted above by NATS)
4) there was no "LAND AT THE NEAREST SUITABLE AIRPORT" so crew flew to JFK in coordination with their OPS
5) who says you are not allowed to divert to JFK or other busy airport?
6) if PIC would have carried on and FAA found out, PIC could have been fined and AA lost ETOPS thus costing millions of $
7) non event