Huh.
The first and only time Virgin America reported a quarterly profit was in the 3rd quarter of 2010. Until they show a real profit, their financial situation is deteriorating, not improving.
When Southwest airlines was formed and almost immediately went public in 1971 they offered 650,000 shares at $11 a share. That's $7.1 million market capitalization, which pretty handily covered their startup expenses for their 3 airplane operation. I don't think you want to make a comparison there.
Nobody has claimed a company never went public when carrying debt. That would be an absurd claim. I think someone claimed no company ever had a successful IPO while so deeply in the hole. I think that's probably a valid claim. Debt doesn't just magically go away in an IPO, the IPO would have to raise enough money to pay it off and also fund future growth. In this case we are talking about in the range of over $1 billion dollars (cue Dr. Evil finger gesture). Their operation is too small to support such a valuation. Delta airlines, currently the most valuable airline in the US in terms of market capitalization, is hugely profitable, is valued over $8 billion dollars, and flies roughly 250 *billion* airline seat miles annually. Virgin America flies roughly 10 billion airline seat miles. It's only 4 percent of the size of Delta, so there's no way they're 12% of the value particularly when they can't make dime one.