Southwest did not pay for travelocity to list its flights and the system was never a live system. Passengers would book on travelocity and travelocity would forward the booking to Southwest. Most of the time it worked but there were times the seat inventory sold out before travelocity forwarded the information to Southwest to process. The result was passenger showing up at the gate with a "confirmed" ticket and there being no space on the flight.
Southwest ended their relationship with Orbitz becuase of unhappy customers holding invalid tickets.
Southwest uses Sabre to process all of their internal operations. Becuase Sabre charges more to show seat avaialbity in the CRS systems, Southwest does not fully participate. Orbitz system uses other CRS systems and direct access into some of the member airlines computer systems. The added cost for Southwest to allow Orbitz to gain access into their system would drive up their overhead cost.
The main reason why Southwest sued Orbitz was due to faulty information being shown on the Orbitz sight.
If Travelocity could not create a workable system with Southwest, I doubt Orbitz would be able to do any better.
Southwest also has the strongest web site bookings of all of the airlines. They want to conentrate on growing this even more since this is the cheapest way to sell tickets (why do you think they offer double rapid rewards for internet bookings?). There would be very little incentive to have Orbitz sell tickets for Southwest.