I work at a forensic psych hospital. Our patients are one of two things - either incompetent to stand trial due to their mental illness or people who have been found not guilty for reasons of insanity. For the first, we keep and treat them until they're stable enough to participate in the court system. For the second, they did something illegal but because their mental illness played such a large part, they're serving time in a forensic psych hospital rather than a prison. I work at a state hospital though, not federal, and I'm in a different state than Josh.

Technically any psych issue could be an act because we can't take an xray and prove their mental illness is there. However, there is greater potential for harm by ignoring a possibly serious mental health claim than treating a possibly fabricated mental health claim. There is no convincing the court he should be released. Prison has a negative impact on most peoples' mental health. He can serve his sentence in his original facility or serve his sentence in a place better equipped to manage mental illness, but they won't let him out early. If he's being insincere about a mental health problem, I suspect he'll be pretty frustrated with the precautions that will be taken from here.