Well as for the discussion as to the photo being private or not, I'm not sure if it was explained here on A am where the photo came from.
The photo of her back, was posted publicly on TinTin's website. There is a "VIP" section where the tattoo shop showcases the different celebs they have done tattoos for. And when you click each celebs photo, it then displays a picture of the tattoo they had done.
So when you click alizee's name, that photo is displayed.
http://www.tin-tin-tattoos.com/home.php
So as far as we know...its OK to be posted, sine I would hope TinTin would have gotten permission before posting it on his site. And for those who don't know, TinTinis the artist who did the tattoo.