It is true, in one sense, that the Holy Scriptures are the product of the Church. Every inspired man that wrote them is part of the church universal. Of course, since each man was directly inspired by God, the Scriptures are ultimately the product of God. Jesus, the Word of God, is the personification of the Scriptures.
As for the Bible agreeing with Roman Catholic doctrines, there are many I just can’t honestly reconcile. I can’t see Scripture agreeing with such things as a physical place between hell and heaven called Purgatory; I can’t see it agreeing with Mary’s immaculate conception; I can’t see it agreeing with the concept of an overflow of grace by exceptionally holy people being dispensed to those of us whose good works don’t outweigh our bad; I can’t see it agreeing with calling upon the dead (which is actually strongly forbidden in Scripture); I can’t see it agreeing with use of images in worship. . . there’s a lot I can’t see in agreement.
This is not to say that every Roman Catholic doctrine is unbiblical in my view. We have a great deal in common.
My main point, which was my first point, is that I see all differences between Roman C’s and Protestants as being rooted in our view of the authority of Scripture vis a vis the authority of the cardinals/Pope/Holy See.
But to be clear, just because I don’t see the authority of elders or bishops being OVER Scripture, - I still believe they have authority. It’s just that I see the authority as being limited by Scripture.
Similarly, a father has authority over his family. But it’s limited by Scripture, too. It’s not absolute.
The Church does not teach that it is a physical place; it is rather a state of the soul on its way to heaven. See 1 Cor.3:10-15 where the process of purification is described.
I can’t see it agreeing with Mary’s immaculate conception
But how is it disagreeing? It is not taught directly, but the fact that she is the only human in history God created for His own mother, it is logical, plus there is the fact that the Angel in Luke 1 describes her as already filled with grace.
overflow of grace by exceptionally holy people being dispensed to those of us whose good works don’t outweigh our bad
On superabundance of grace, see Rom. 5:19-20.
calling upon the dead
The Old Testament forbade necromancy and making of idols (not necessarily images), but neither prohibition is repeated by Christ (He repeated and strengthened the rest of the Ten Commandments) and many -- such as prohibition of eating pork -- are abolished according to the scripture. Logically, since Christ gave all of us enternal life, the saints are no longer among the dead, and the chasm between those alive in Christ and us no longer exists. Praying to the saints is at least consistent with the Christian scripture, even if not directly described in it.
use of images in worship
How does it contradict the scripture (making of idols was for worshiping idols)? Christ Himself in several places is described as an icon of God. There are two direct prooftexts sancioning the use of images for worship, 2 Cor. 3:18 and Gal. 3:1.
Overall one can argue that there are things in Catholicism that are not derived from the scripture directly. But neither does Catholicism teach that everything in Christianity should be derived from the scripture directly. Protestantism, on the other hand, teaches that, yet its foundational doctrine of "sola fide" directly contradicts the scripture, and the other one, "sola scriptura" is not contained in the scripture.