It is 30 days, not 3... Nel misspoke.
I think he is calling his bluff....
You want to pretend you have a mental problem, FINE - go to the mental institution, get prodded and poked and listen to the inmates howling at the moon and lets find out for real.
As Nel says to Roux - "this was your idea, you bought the shrink, now I need to test the evidence".
Roux however has one thing on his side - OP has admitted he knows right from wrong, the shrink says he does, he doesn't claim memory loss, he doesn't claim insanity as his defense, he doesn't claim have had a psychotic episode.
Nel is one step away from having him committed and I do not think he will succeed. Just my opinion.