Real, or fake email? WoW only email.

A while back my wife and I were hacked. After regaining our accounts we ran every virus/malware program under the sun, formatted our PC's, and even changed our email addresses to ones ONLY used for World of Warcraft. So far I haven't received any fake emails or the like in the new email, just 15 messages from blizzard about account changes I've made. However -- I received an email that was labeled by hotmail as junk and the contents are,

Hi --------,

My name is --- and I work with the Customer Care & Loyalty team here at Blizzard Entertainment. While going through some cancellation data I came across your cancellation notes and noticed that your account had been compromised. I see that you regained control of your account and are actively playing but I wanted to see if you were interested in a free Battle.net Authenticator for additional security. Please reply back with a phone number and time I can reach you at. I am in office M-F 9am to 6pm PDT. If you do not require any assistance please feel free to let me know with an email reply.

--- ----
Customer Care and Loyalty Agent
Blizzard Entertainment
-----@blizzard.com

Names are taken out since I'm not brushed up on forum policies.

Can I get a confirmation on whether this is real or fake?