NPR Stations in the Same Market Running the Same Programs at the Same Time:

I like listening to All Things Considered and other NPR shows; I'm not wild about their political bias, but I like their tone and style. Another example of cultural affinity trumping political affinity, I suspect.

But here's my question: In L.A., two radio stations (KCRW and KPCC) both carry All Things Considered, but they generally carry it at the same time. That means that if there's a story on one station that bores me, I can't just switch to the other station, since the other station is generally carrying exactly the same story at the same time.

Now of course neither station wants to give up the optimal time slot -- but why doesn't one station (perhaps the one that has fewer listeners and thus more of an incentive to try to get some) play the segments in a different order? Unless I'm mistaken, the NPR news feed is 2 hours long. Why doesn't the less popular station play the second hour first and the first hour second, and thus suck in the other station's listeners who want to switch away from some boring story? And if they're above mere listener-grubbing, why don't they just provide such an alternative as a public service?

Is there some technical or contractual twist that I'm missing? (I don't think there's any antitrust problem, because there'd be no need to have any agreement between the two stations; either station can do this unilaterally.) Please respond in the comments.