I remember that episode of his tv show, though as I recall, he was talking about Bo and mentioned the “White House dog”, then his producer put up a pic of Chelsea. Who knows if Rush was in on it or not.
The write-up at the link explains what happened. Doesn’t sound like it was intentional to me. And Al Franken’s account of it in his book, which is how most most people are aware of it, is certainly incorrect. BTW, that Franken book is the one book you can count on all liberals having read.