Codeshare fares are set by the carrier selling the ticket, regardless of who is operating the aircraft. So HU could have lower fare buckets available that AA doesn't. Or HU could have a sale that includes this route, but AA might not sometimes, it might be the other way around.

Unless this is part of an ATI, the partners can't set fares or collude on which buckets are open. And short of one airline matching a sale from another, no airline is going to match a price of another by calling and asking. Just like AA wouldn't match an ORD-DFW fare UA has by calling and asking.