Actually, given your intended scenario, it's much more likely to be that because we've indiscriminately and randomly bombed a bunch of uninvolved people, we've recruited a bunch more bad guys from the vast majority of people who wouldn't really have cared in the first place. It's the same way that holding people in prison for years because they were sold to you for bounties pretty much ensures if they weren't America hating terrorists before, they certainly will be now.
It's not rocket science -- reverse the positions and put your innocent self in the scenario. What would you do if BigGov put you in jail wrongly for many years, or killed all your family because one of the neighbors was a criminal?

