That's a good idea but a number of stations across the country don't carry the program live. Her 'exposure' could have been from a taped program. Still...easy enough to make inquiries IF one knows the station doing the broadcast.
I think the FCC requires broadcast outlets to compile logs of all of their broadcast activity. Easy to look up at each local station.
Heck, I would bet big money that the entire transcript of the show for that date would show nothing remotely racist was in Rush's show content and would easily disprove the charge. But I would be very interested in specific time periods to prove this lady is full of it.