I'm a proud lurker (2 or 3 posts in several years), so I'll say my piece and then crawl back in my cave. I'm a Marine and I've worked with a sh'load of civilian contractors overseas. I don't think you can paint the picture in terms of overseas jobs being more 'attractive' than domestic jobs. People have been working for years supporting military operations. I will point out three things:
1) Many of these people are retired or former military (many, not all). It's a natural chain of events that they stick close to the connections they made while serving. Military service contracts and DOD civilian positions are the easiest to get for people who have been in the military and already know the system
2) Many of the contractors I knew in Iraq had children in the military and they took jobs with KBR and others partly as a show of solidarity with their children. I remember being surprised at how often I ran across this... I would say this was a factor for 40% of the truckers I worked with in Iraq
3) Deploying in a civilian capacity as a contractor has tons of perks that are difficult to match regardless of how good the economy is in the US. Contractors get free food, lodging, health care, and entertainment from military providers. They have VERY high salaries (almost without exception in the 6 figure range). And they don't pay taxes.
Apples and Oranges.
To all my fellow Devil Dogs out there, HAPPY BIRTHDAY