Since the OP gave a physics example, here is another one, also at Princeton. Why are they always at Princeton? Student finishes his presentation on very mathematical aspects of string theory. An experimentalist on the committee asks him what he knows about the Higgs boson. He hems and haws and finally says "well, it was discovered a few years ago at Fermilab", Experimentalist: "Can you tell me the mass?" Student: "I think around 40 GeV."
This was more than 20 years ago and actually happened. I was there. The student passed, but the next year all Ph.D students working on string theory were required to take a course on the phenomenology of particle physics.