Update [3:37 PM]: It is currently believed that this is only sharing an internal account ID number that Blizzard uses. However, Blizzard's database has been hacked in the past. For further information, there is a reddit thread and the link below has comments.
That said, it should had a further layer of caution to those posting screenshots, make sure you aren't violating any NDA's.
It is a clever method...I wonder how much it has been used.
While perusing news on the web today I came across this article:
Regarding Blizzard secretly marking your screenshots with artifacts. As I know many bloggers like using screenshots in their posts I thought it would be timely to warn that apparently some information might be leaked as a result. I hope there is nothing to this and that it is all just a rumor, but when it comes to account security I tend to prefer a proactive approach to a reactive one. One guild member getting hacked was enough for my taste.
So consider this my call to bloggers to be extra careful about the screenshots you post!
I wish I had more time to post on this but I am at work, though it is somewhat alarming that Blizzard is sneaking this functionality in without any notification in the ToS or EULA. I see why they did it; most likely it is meant as a protection of NDA's by allowing them to figure out who posted the picture (especially of unreleased content) so they can take proper action...but this opens up another can of worms.
I'd recommend getting an authenticator...really, it's easy, they're cheap (free for your phone if you have an Iphone) and they come with a cute pet...there really is no reason not to and you do NOT want the experience of being hacked, no matter how cautious you think you are being.