This claim doesn’t make much sense from the outset. Look at your specific example of transistors. In 1965, an electronics magazine wanted to figure out what would happen over time with electronics/transistors so they called up an expert, the director of research of Fairchild semiconductor. Gordon Moore (the director of research), proceeded to coin Moore’s law and tell them the doubling would continue for at least a decade, probably more. Moore wasn’t an outsider, he was an expert.
You then generalize from an incorrect anecdote.
It wouldn’t have made a lot of sense to predict any doublings for transistors in an integrated circuit before 1960, because I think that is when they were invented.