I find this story unlikely, but probably for a pretty uncommon reason. Here's the thing: I heard this question a number of times before (never in an interview; always on the interwebs), but never attempted to solve it and never read a solution. As I was reading this paragraph:

  Can I assume that the lights and the switches are correctly
  wired according to the National Electric Code of the United
  States? That is, that the switches interrupt the hots, not the 
  neutrals, that the switches are standard-duty switches rated 
  to interrupt 15 amps of 120 volt alternating current, and so on?

I instantly realized the intended answer. I don't doubt for a second that if that just happened to me, it would also have happened to Feynman (because I blame being a physicist for what just happened), immediately after first thinking of that important signalling word that he was supposedly about to speak.