People who say they know themselves can be categorized as either down to earth or misguided. I think the latter categorization is the only plausible one.
The self doesn't exist. As a matter of experience, we are processes, not tangible selves riding around in our heads. We are compelled by thought to act in certain ways depending on our situation. The decisions we make, how we navigate the world: that's who we are as people. This is a complicated and expansive definition of who each of us really is. People can't simply be categorized and constrained as a self by the definition we place on that term today.
Since there isn't a self to know, you can't really know yourself.