What exactly qualifies Napolitano for this office?
Well, as I said before, two of the divisions of the Department of Homeland Security are the INS and Customs, and as a border state governor, she's probably forgotten more about illegal immigration than most people know. Also, the DOHS is responsible for the National Parks, and there are several in Arizona.
If it looks like I'm grasping at straws, I'm not. It's just that the Department of Homeland Security has nothing to do with Homeland Security, and everything to do with miscellanea.
Yeah, a lot of people seem to think that "homeland security" sounds rather orwellian, and consequently think that it's all about wiretapping and such, which is way way off the mark.
The reality is that Homeland Security isn't about security at all. Even as far as it deals with national emergencies (which are hardly daily affairs, and may not even happen once per President), its focus is on dealing with disasters after they happen, not with preventing them. Preventing disasters belongs to Defense, via the CIA, and Justice, via the FBI (except natural disasters, obviously, which can't realistically be prevented).