I could be wrong, but I bet the govt generally gets the developers of the systems / software themselves. So the developers of various linux kernels, CISCO firewalls, etc.
However, the guys who actually hack into places like Target, Sony, Microsoft, banks, etc.??? They're generally 100% completely anti-govt and anarchist, so aren't about to take a say $8000/month job with the govt. Maybe I'm wrong, but I'm assuming the main way they recruit these guys is via plea bargains within the interrogation room at an FBI office after they've been caught.
And the two are somewhat totally different types of people, with different mindsets. They're hurting for the latter, not the former.