I flew with her on a SW flight when she was running for Senate in CA. Southwest is actually the most efficient way to get around that state with 9 available airports, so no wonder she is a SW fan. Even the Gov Jerry Brown flys SW.
You will not find any of the Presidential candidates flying First Class when they fly commercial...it is a perception issue. They will do business class at best.
Only Hilary, Jeb and Kasich fly private on a regular basis (and Trump, but he OWNS his plane so that does not count)...none of the others have the bankroll to go private at this point so spam can with the rest of us it is!