Authority, etc.

I've only just begun to study the fascinating postings on authority, etc., but one question occurs to me right away.  Don't the Church's own careful distinctions as to the kind of adherence she asks of the faithful matter to analysis?  An alternative taxonomy, helpful in itself, has been developed in the conversation here, but I'm not clear on how it tracks or declines to track what the Church herself has taught on these precise questions.  The Church's distinctions may prove to be inadequate to our purposes here, but in a tradition that knows how to "define and declare," pronouncements of other kinds should be treated as what they claim to be.  Perhaps there are straw men in operation here and there?  For example, the Church claims the authority to teach unerringly what is contained in the deposit of faith.  But does she claim to teach with equal certainty what is not explicit in the deposit of faith but is known (only) thanks to the natural law?