We're certainly better at reflecting at some parts of our self than others. The ironic thing is, though, that when we look more closely and analyze just what it is that we are not reflecting on very well that we open up the can of worms that we had previously been avoiding.

In the context of the original post - suppose that SGAI is logging some of the internal state into a log file, and then gains access to reading this log file, and reasons about it in same way as it reasons about the world - noticing correlation between it's feelings and state with the log file. Wouldn't that be the kind of reflection that we have? Is SGAI even logically possible without hard-coding some blind spot inside the AI about itself?

If we could we'd probably have gone extinct already.

Or maybe we're going to go extinct real soon now, because we lack ability to reflect like this, and consequently didn't have couple thousands years to develop effective theory of mind for FAI before we make the hardware.