Ollie Onion, agree with you on the doubt re the rumours of QF on JQ bills. Reality is most people on the ground won't see the bill they will just know that ex QF staff did this for JQ etc.
However if I was Simon Hickey, CEO Qantas Intl or Lyell Strambi, CEO, Qantas Domestic, I would be making darn sure, given that undoubtedly my pay/bonus/potential promotion to Group CEO depends on the profit of my individual business unit that I would be sure making my unit got paid for anything they did for what is effectively a competitor (albeit part of the same umbrella).
And I don't see any particular issues with divisions competing against each other, each with a slightly different market segment target. I look at
Wesfarmeres - Kmart v Target
Leighton - Leighton v Thiess v John Holland
Westpac - Westpac v StGeorge/BankSA/Bankof Melbourne
Lend Lease - Lend Lease v Abigroup v Baulderstone
All companies that are far larger, and I daresay more complex than Qantas