Isn't self inquiry just another form of seeking?
Someone might consider self-inquiry to be “seeking,” and I can see that. But the emphasis is that there is no reliance on outside authority.
With inquiry you neither accept or reject anything. It is just there. You see it for what it is, but if your thoughts are involved, with your preferences and prejudices, you are still enslaved to an outside authority. (Thought, in this case, is an outside authority disguised as the self. It moves within itself, and its range is limited and outside of awareness.)
Does that make sense?
Things are not rejected because of what you know. Rather, they fall away on their own, when seen as they are.
(Although the "self" in self inquiry is not quite right, I still use the term, but more often than not, I'll just use inquiry.)