a smart phone is orders of magnitude more powerful than a mainfraim computer from the 1960s that took up a large air conditioned room. That's part of the problem. How did they navigate so precisely with a substandard on-board computer? Granted they developed the microprocessor to make it happen, but it would have been less powerful than the first Apple machine delivered in the late 70s.
In 1978 people were still using card punch machines to create computer programs to be read through a card reader connected to a mainframe.
This lack of power and sophistication is partly why the conspiracy theory exists. Couple with that with the fact that the space program through the rest of the 20th century (after apollo) amounted to low earth orbits with the space shuttle.
Finally with all our technology and powerful computers, with our advances in machining, look how long it is taking to create a set of new rockets to launch man into space.
I'm not saying I believe the conspiracy theorists but I certainly understand how a dismal space program (after the pinnacle reached by apollo) creates fertile ground for their theories to take root.
"Mainfraim"? Nice typo there. Reminds me of a Delaware County, PA bowler named Elmer Fraim...
https://www.delcotimes.com/news/gebhart-ex-ridley-bowl-manager-strikes-out-at-today-s/article_56b7bf9a-d702-5559-b542-0ff61e1bcef8.html
or if you hit the paywall...
https://outline.com/pYYyMR
ff