In my view, security is just another part of the user experience. For one's bank, it's surely a large one. For most web services, though, it's pretty tiny. As a Quora user, I'm perfectly happy for them to increase usability substantially at the cost of a minor increase in risk.

Yes and no. Of course security is important, but no realistic system is ever known to be completely secure, so it's always a cost/benefit question.

If you take security far enough that your system ceases to be useful, then UX certainly won't matter, because you won't have any users.

More commonly, if you make security checks too disruptive, it can be counter-productive because users will start to circumvent the system. Consider all the stories you've heard of someone changing their "updated monthly" password by just adding the next number on the end, or writing the PIN for their credit card on a bit of paper they keep in their wallet, or having a note of their network password taped inside their desk draw. Or just be the guy at Microsoft who invented UAC in Vista. ;-)