The Three-legged Stool of Roman Catholicism Adds Up to: Sola Ecclesia

I've seen a few cyber-buzzing's about the Protestant use of the term, sola ecclesia. The phrase is said to be inaccurate because Roman Catholicism holds to the "three-legged stool" model. As someone who has utilized the phrase "sola ecclesia" when evaluating Roman Catholicism, here is why I do so:  

Sacred Scripture: the Roman Catholic Church infallibly decided what books are in the Bible

Sacred Tradition: the Roman Catholic Church infallibly decides which traditions are authentic "Tradition"

Magisterium: the Roman Catholic Church claims to have an infallible Magisterium that serves as an infallible teaching authority.

Each of the legs of "three-legged stool" all boil down to the same infallible authority: the Roman Catholic Church. If Roman Catholics want to use the "three-legged stool" analogy. I suggest that it would be more accurate to say, "upside-down three-legged stool." 

If you are a Roman Catholic using the "three-legged stool" analogy, would you be please let me know where this analogy originated? From a cursory search, its origin is murky, with one website claiming a version of it originated in Anglicanism ("holy scripture, sacred tradition, and our God-given gift of reason"). I spent a few minutes on the Vatican website searching the phrase "three-legged stool" and did not get any meaningful hits. 

Google AI isn't always accurate, but if it it's correct, it would be rather ironic that the analogy was taken from... Protestantism!