No, this IM shows that deep down, Zuckerberg _does_ care about privacy, and that he thinks other people should too. He disparages people for giving up that privacy.
Um... what? If this exchange is genuine (the source is extremely vague), it shows that, yes, he probably values his own privacy, but not anyone else's. If he thought "other people should too," he would be campaigning to inform people about privacy concerns, not actively destroying their privacy for his own benefit.
If you're a burglar, you'll probably make fun of people for their weak home security. You don't want your house broken into, but you sure don't want everybody else getting smart. This hardly shows that you "care."