I found an attorney site that explains this confusing term. This is the site I mentioned about the "cobra in the cell" scenario:
http://www.wlv-online.com/what_is_deliberate_indifference.htm
This is the reference I found in the HBO prison drama Oz:
http://www.youtube.com/watch?v=go4ARLwxDYA
The reference to "deliberate indifference" begins with an exchange between the character of Tobias Beecher (former inmate and disbarred lawyer, now employed as a legal assistant) and Henry Stanton (an inmate who injures his back), beginning about about 1:10 into the video. About 1:45 into the video, Beecher states that the C.O.'s probably violated Stanton's "rights under the eight amendment, deliberate indifference."
I'm no constitutional lawyer, but I wasn't aware that the eighth amendment covered any such thing. Unless he's referring to a state constitution.
But not really an earth-shaking issue. I was just was just fascinated by this new and contradictory term. Malaprops, redundancies (such as "irregardless"), and contradictory terms have always entertained me. And I was just delighted to find a new one.