That’s not why she read the manuals. She read them for job security. Computers were going to end their jobs. And I don’t think it was IBM engineers that were the problem, but NASA engineers who weren’t up to speed on these “new” systems.
Exactly what did she do at NASA?
In the pre-computer days, I read that places that needed calculations done on raw data. (I’ll call it numerics! )These places like the Census Bureau performed their numerics with floors of people (usually women!) reading the data off paper records and using mechanical calculators to reduce the data to something that could be used (if the Census Bureau) by statisticians. Since this is the 1960s its at the cusp of the computer revolution, did she take raw data code it up (Fortran, assembly or binary?) and run it on main frames? Then give the results to the NASA (or contractor) scientists? If so that’s great! An important contribution to the team. However a lot of other people did similar things & I see no movies about them!