Last fall I flew an AA flight on which I rented an Avis car with a WN (SWA) promo, and also flew a WN (SWA) flght on which I rented an Avis car with an AA promo. Both worked fine.

(The reason for the flip flop had to do with the number of rental days being different between those two trips, and each promo requiring a different number of days to get maximum bang for the buck. In that case, for me, the AA promo worked better for whatever number of days I was renting after the WN flight, and the WN promo worked better for me for whatever number of days I was renting after the AA flight.)