But that doesn't mean you can't make your own connections and many people do. They just have to claim any checked luggage they've checked with Airline A at the connection point and recheck it with Airline B for the continuation of their trip.
Domestically, people flying Southwest out of DAL frequently do it when flying from DAL to cities outside the Wright Amendment.
Internationally, people fly Southwest to LAX and connect to International flights to Asia. There was even an episode on A&E's Airline where a Southwest flight had arrived late and an Asian couple was trying to make it over to the International Terminal to make their connection. (In that particular story, they missed their connection but I don't think that's the norm.)
Given the choice, most people would rather be checked all the way through by the airline. But if the price difference is great enough, some people will book it as two separate trips and handle the connections themselves. I think the point that Malaysia was trying to make is that by flying to SFO, SEA and LAX, Independence Air might be able to capture some of this traffic.
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