I think this is the correct explanation. Can someone find a counter-example where "no" is used in the weird way the New Yorker piece is describing, but where it can't be taken to mean "No, you don't have to go on; I know exactly what you're talking about/asking"?

The example given by yathern...

> A: I wasn't sure if you'd like to go to the park - do you want to?

> B: No, totally! Definitely want to go.

...seems to fit.