Earlier quoted context omitted.
Feynman is great, very amusing and obviously brilliant. But I've also worked with folks like him before who end up as fish out of water in fields they don't know the conventions for and can't be bothered to learn. Lots of time is wasted trying to figure out how to get the rest of the company to communicate with the lone genius, and it's obvious that they're smart enough to go away for a week and learn enough of the f…
Well actually in the next few paragraphs they do end up trusting Feynman's analysis and go with 5. And it worked.
They only used 5 when it turned out they couldn't manufacture 7 and had no other choice. So they only trusted his analysis out of desperation / wishful thinking, not out of objective reasoning.