When on New Caprica, can a crisis effect move a player from Detention to the Medical Center?
I'de say no.  Even thought the rules don't spell it out explicitly I think it's clear enough.

First, detention and the bring are treated to be the same thing, especially for player powers.

Second, according to the FAQ (page 2, bottom of the first column) nothing can move a player out of the brig except a successful skill check for the brig location action.  So by extension this applies to the detention center.

Third, thematically it didn't happen (spoiler follows).


   When Tigh was in the detention center and Cavil ripped his eye out, he left him there.  Even when he kicked the snot out of him as well he left them there.  He totally should have gone to the medical tent but didn't.