I have used an authenticator for about 6 months now. I use PC's at two different addresses to access WoW; albeit on the same ISP.
I recently got my hands on a netbook powerful enough to run WoW (specifically - I can post auctions on it). I broke down and purhcased the Curse premium client to make it easier to sync addons and settings. I finally set up my mobile phone and netbook so that I can use the phone as an internet access point.
This morning I attempted to log in for the first time using the phone as a wireless modem.
Our login system had dectected a change in you access pattern. In order to protect the account we require you to verify your identity and change your password via our website For more information plase visit (link provided)
I suppose I understand the test. It would provide a barrier to an account hacker. However, in terms of account security; I already had a authenticator. I thought this was meant to assist in positive identification. Blizzard's decision to insist on an email address as a login code is terrible from a security point of view; I was asked 4 security questions; If you know my login code you already know 3 of the answers.
The fourth question was a choice of cd key from the install CD's (original and expansions), or a previously set up security question. I was on the road so didn't have any hope of a cd-key. I am pleased that I remembered my security question that I set up years ago.