I've always suspected it was apocryphal. But just think, if the workers had installed that fan beforehand, we might be reading a story about how important workers are at solving little production problems.
Everyone thinks this mentality of having workers fix problems is great, until they use soap to put glued parts on.
"I sleep on the floor" .. "You're fired for not proactively fixing a problem I just thought of a solution to". Is my speculation off-base?