For what it’s worth, inaccuracies can be found in movies of all genres if you look for them. In "Bottle Shock,” a movie about the 1976 Judgement of Paris wine competition, there’s a scene that was filmed at Chateau Montana, a winery in California. If you look in the background you’ll see wine fermentation tank controls that, I’m told, where installed by Hale Winery Refrigeration. Unfortunately those tanks hadn’t been installed when the events in the movie took place.
Sounds ridiculous, right? Like, who the hell cares? I suspect that's how 99 percent of the viewers of "Sully" would respond if told about the inaccurate Phantom.
Sometimes I think our knowledge about a subject can get in our way of enjoying a simple movie.