>> “Please upload a photo of yourself that clearly shows your face. We’ll check it and then permanently delete it from our servers.” >> To determine if the account is authentic, Facebook looks at whether the photo is unique. I assume this means that the photo itself is deleted but a one-way hash of it created to test against later. However, if I change one pixel of a picture of my face, A, to produce a new picture of…
Hashes don't necessarily work on the raw bit representation of something. You can have a hash which works on higher level constructs, which for images one solution would be called a perceptual hash.
I'm sure it's still possible to steal a picture from someone else's online presence outside of facebook though and upload it as "unique" and facebook won't have any way to know that, unless they scan every other social site (and the rest of the internet, possibly).
And someone could always take a picture of someone else's face, with a bit of social engineering, and use it to get access to their facebok- although I don't think that's the kind of thing facebook want to detect here.