I always fly United but I tried SWA today.
You are assuming the airline you are flying would have any effect on the handling operator selected. This has never been the case, since GSX came out, since it would be very unrealistic to have your own crew following around all over the world, when in fact ground handlers are only related to the airport.
The airline you are flying ONLY affects the livery on the ULD containers, assuming your aircraft.cfg contains the parking codes that matches operators available in GSX.
According to GSX inbuilt operator rules, the operators available at KHOU are ATS, GAT and Trego-Dugan. We only added Trego-Dugan recently, but in previous versions you would only see ATS and GAT, since SWA has a very low priority.
Of course, you can set any operator you like at any airport, in the parking customization page, which will override any inbuilt rules.
