Yeah, I seem to recall that while the full report took some time (because they always do), the fact that everyone's stories matched up with the flight data recorder and the physical evidence meant there was no real question as to what had happened. I do recall there was some debate over whether the aircraft could've returned to LGA, but checking online it appears the FAA and NTSB concluded that it would've required foreknowledge of the event and unrealistic actions on the part of the crew, and even then only had a 50% chance of success.
That said, this is the second hagiography Clint Eastwood has made in a row, with American Sniper being one of the worst films I've seen in some time. I am concerned that he is falling into making propaganda rather than trying to share interesting stories.