Which airline said, "they don't need assistance?" Or even, "they don't want assistance?" Only quotes I have read and seen are from the A4A group where the airlines said they would support more assistance from the gov as long as they didn't attach any new restrictions tied to them. Airlines do want another round of assistance because when they play by the rules and regs for getting said assistance they are usually turned into grants as long as they stay away from the layoffs, furloughs and pay cuts.
Now if you are referring to SWA saying it, I don't recall that. I do recall that it was stated that SWA has enough cash to last 2 years with the current amount of losses, but that's not saying they don't want the assistance. Matter fact SWA has spoken up in support of the unions asking for further assistance and an extension.
I could also see AA and possibly UAL not accepting that assistance IF it is voted to extend it, as they know that they would have to layoff and/or furlough and cut wages and benefits to still get the airlines "right sized". AA has already said no matter how many take the outs and leaves that they will still be 20,000 employees too heavy and that is most likely due to the merger with US Airways that they never did shed. Just not sure about UAL's intentions, but with almost all of their mechanics getting notices as D757 said, it does look like they are CYAing and are preparing to do what AA is going to do come Oct. 1st.
Here's more from our CEO. Nowhere in this memo does it say anything about not wanting assistance or an extension...
https://www.yahoo.com/news/southwest-ceo-says-airline-intensive-183927566.html