What it comes down to is simple: The cost of losing one plane and its crew to hostile fire in Iraq is so much less than the cost of losing the US Armed Forces contract that Falcon management are prepared to roll the dice and hope it doesn't happen.
The problem is that one day it will happen - tragically that'll be the only way that the firm's "fearless leaders" learn from their repeated mistakes.
Until then beating your head against barbed-wire would be more effective than trying to challenge the status-quo. Better just to go to work, rack up the hours and get out as soon as you find something better.
Remember: "No quick hands"!
P.S - I'd almost be more concerned about operating into Saudi than Iraq. Especially after this morning's events in Riyadh and associated diplomatic warnings in Qatar & Bahrain.