I reject your case. Self-identification isn't even necessarily something that's public. It's as much a question of who you are to yourself.
Self-identification is a broad topic. Sports fans create opposition with other self-identified fans for the sheer hell of it. Crack addicts self-identify. Being married is a joint self-identification.
In any case, the redundancy is meant to force the argument to the other definition. My prime point is not that they think they're smart, it's that they're trying to sort people into valid/invalid thinking bins.
And as a side note, there's something very wrong with thinking that social signaling or labeling is a trap.