"He's the man that planted the flag on the face of the moon," Trump said. "There was no kneeling" - a reference to NFL athletes kneeling in protest during the national anthem.
The film was inspired by the authorised biography of Neil Armstrong by author James Hansen. In the book, Hansen wrote about the mementos Armstrong took to the moon. They were few - medallions commemorating the Apollo 11 lunar mission, jewellery for his wife, a piece of the Wright Brothers' aeroplane and his college fraternity pin.
"I didn't bring anything else for myself," Hansen quotes Armstrong as saying.
His then-wife Janet Armstrong was apparently distressed that "Armstrong took nothing else for family members - not even for his two boys," Hansen wrote, adding: "Another loved one that Neil apparently did not remember by taking anything of hers to the moon was his daughter Karen."
Bill Barry, Nasa's chief historian, said questions about the scene came up recently during an event for the movie at the Kennedy Space Center. Regarding the conclusion, he said: "The scene was created for the movie, and there is no specific evidence that Neil Armstrong left any 'memorial items' on the moon."
Though apparently fiction, the moment is a critical one. Throughout the film, Armstrong, who died in 2012, is portrayed as a stolid and steely pilot who keeps his cool in all sorts of stressful situations.
The death of his daughter from a brain tumour, however, serves as an emotional undertow, a recurring theme in the film that reveals Armstrong's humanity.
Honouring her memory on the lunar surface would have been poetic, Hansen wrote: "What could have made the first moon landing more meaningful 'for all mankind' than a father honouring the cherished memory of his beloved little girl?"
Other Apollo astronauts paid tribute to their families on the moon. Eugene Cernan, the last man to walk on the moon in 1972, wrote his daughter's initials in the lunar dust before he departed. Buzz Aldrin carried photos of his children, and Charlie Duke left a photo of his family on the lunar surface.
While there is no evidence of it, it is possible Armstrong did something, as well - and that is why Hansen said he is okay with it in the film. "We don't know for sure what Neil did," he said in an interview. "Maybe that's a rationalisation."