Earlier quoted context omitted.
Well actually in the next few paragraphs they do end up trusting Feynman's analysis and go with 5. And it worked.
I think you and the parent are agreeing. :) They didn't know what to make of Feynman's analysis, because it used techniques they weren't familiar with. It was clearly an approximation; were the error terms really ignorable? 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.
Additionally parent comment complains about people like Feynman not being able to communicate. But there is nothing about that in the story. It goes on and on about how Feynman was a great communicator and explained his ideas clearly.