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I can't speak for science, but one certainly doesn't need an advanced university degree, or even an undergraduate degree (Gates, Jobs, Zuckerberg, etc), to do fantastic work in software. People with a masters or Ph.D in CS from a well-regarded university tend to have a certain polish, though, with a practical understanding of the peer-reviewed research and fewer gaping holes in their base of fundamental knowledge. That would be important for professors, as even Dyson grudgingly acknowledges in the interview, I think.

It's almost a truism that many or most of the best teachers on a given college campus are those who don't have tenure. Youthful energy, ambition, receptiveness to new ideas, lack of complacency and habits of political infighting, rapport with students, are some of the reasons commonly given.