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But there is no teaching of Fatima. We have a private revelation about which a secret is alleged (private does not mean it's secret, the term means a revelation outside of the truths revealed to the Church as a whole by God). Rome says, there is no secret and the Fatima letters were published. Either way, it is not like once we know precisely what was revealed to the Fatima children, we shall say a big "aha" and start believing something we did not believe before.

The Church has secrets: every sacramental confession is secret, no matter how long ago it took place. The prelates have their privacy. There are bank accounts, the diplomatic pouch, -- like in any organization. There is no secret teaching though, like for example the Gnostics claimed to have.

Jesus answered him: I have spoken openly to the world: I have always taught in the synagogue, and in the temple, whither all the Jews resort; and in secret I have spoken nothing (John 18:20)