There is an element of truth, albeit tiny. The NTSB did show that it was just barely possible for Cactus 1549 to return to LaGuardia. Yeah, the movie did ramp up the drama but the NTSB did initially still question his decision to ditch the plane, although they came around to it pretty quickly. In their report, they stated
"the captain’s decision to ditch on the Hudson River rather than attempting to land at an airport provided the highest probability that the accident would be survivable.”
According to the NTSB report, Airbus replicated the turn back to Runway 13 at La Guardia 15 times in a simulator, and pilots were able to get back and land 8 times. They also simulated a divert to Teterboro nine times and succeeded just once. While La Guardia was the best option of the two, the sims showed that as 50/50. Sully testified that while returning to La Guardia was an option, it would have been
"an irrevocable choice" that put him out of options if he couldn’t make the runway there. It would also put people on the ground in densely populated Manhattan in grave danger.
Its also worth noting that just one of the sims incorporated the 35-second delay to account for the pilots’ reaction time and for running through the
"memory Items" and the QRH, and it didn't make it anywhere near the runway, crashing 3/4 of a mile short.
It is also true that starting the APU is not a "memory item", its the 11th item on the QRH checklist. Sully's inspired decision to immediately start the APU ahead of the checklist was probably the single most vital step in helping to save the crew and passengers.
Finally, Airbus released their own report and in it, stated
"Although an emergency return to La Guardia Runway 13 was technically feasible from an aircraft flight performance point of view, the emergency landing on the Hudson seems the most appropriate decision."
For anyone interested the report on the Cactus 1549 accident is here...
Warning: This is a 6MB PDF
https://www.ntsb.gov/investigations/accidentreports/reports/aar1003.pdf