I have had them put me on AA
Last year my family vacation to Hawaii hit a typical UA snag. MX on the outbound from CMH to ORD where I was picking up ORD - HNL.
I got them to put 5 of us on AA citing reg 240 and the fact that I was in a contract with them and they need to live up to it.
It was the 1K desk though, which doesn't seem to exist anymore.