I don't know how old you are but when I was first introduced to programming in the early 80s all "source code" (Mostly basic and thus interpreted where program is the source code) was referred to as "listings" (this was when the main source of games were monthly magazines where you typed in a listing from a magazine and saved it to tape E.G.. The "Program listings" (as the Smithsonian calls them) seem to be print outs of the programs for verification purposes.

The process of entering was indeed handwritten, on specially printed sheets of paper that was then handed to a punchcard operator to create the cards (again according to the Smithsonian), But the stack of paper is clearly not those sheets as it is form-feed printer paper.

It is completely accurate that Margaret Hamilton lead a team, so while there are inaccuracies I'd say this not as much of a lie as just a combination of confused concepts,