This is heart of the problem that today's Catholics are experiencing. They have been taught the blasphemous error that the fullness of truth merely "subsists" in the Catholic Church. This new-age teaching has supplanted the classical-traditional Catholic teaching that the Catholic Church is the truth, and the difference has enormous implications.
"if I am delayed, you may know how one ought to behave in the household of God, which is the church of the living God, the pillar and foundation of the truth." (1 Timothy 3:15)
As the above Scripture verse says, the Church is the 'pillar and foundation' of the truth, meaning that its spiritual structure of doctrines embodies, upholds and dispenses the Truth, hence the Church, (which is a set of teachings), is the truth. When you say that the truth merely 'subsists' in the Church you make the Church and the truth two sovereign entities and compartmentalize one within the other. This horrendous teaching implies that the Church contains or harnesses the truth when in fact she embodies the truth and is woven together by the fabric of Truth. The Church, as the Bride of Christ, is betrothed to the Truth, (Jesus Christ), and the two become one. (I am the way, the truth, and the life").
Furtermore, this modernist teaching allows that the truth can 'subsist' in other churches and religions as well, since it is not restricted by the totality of Catholic teachings. In thier view the truth can be sliced, diced and spread about in bits and pieces and fed like French Fries to people instead of the whole potato of revealed truth.