Thanks dorrien for the nod and the clips (the Reagan story is quite well known over here). Clue was sadly all too topical, although Harvard is the Cambridge university more in the crosshairs at the moment.
Chris, I've seen MIT = Cambridge university more than a few times in published crosswords; I think if I was referring to the UK one I'd have to capitalize "University". In fact I used this device in my latest puzzle, which there's still time to work! (Shameless plug.)
https://crypticcrosswords.net/puzzles/ntspp-puzzles/ntspp-792/