That is exactly how it works in the Catholic Church. The command to "believe" in Jesus Christ for salvation is defined as believing in everything the Catholic Church declares must be believed in order to be "in communion" with the Church. Only those who are in communion with the Church (the ONE, TRUE church that Jesus established at Pentecost, according to them) can merit eternal life. Slowly, through the centuries, this rule of faith has expanded to include doctrines not even heard of in the Apostles' time nor even the first several centuries after their deaths.
You definitely described the point that, for Catholicism, the only fruit being inspected is that which they decide IS fruit (i.e., going to Mass, Confession, Penance, corporal and spiritual works of mercy, etc.). It's only been in the last century that the hierarchy has acquiesced to the truth that Christians exist in other faith "traditions" besides Catholicism and even that is disputed by the more traditional Catholics, who reject Vatican II, or at least the interpretation of it. This exclusivity is not Scriptural nor does it honor Jesus Christ.
Ultimately, it comes down to authority. Catholics believe in the authority of the Paraclete, exercised through the Magisterium, you don't. Protestantism ascribes to itself the abilities to interpret Scripture that it denies is possible in the person of the Catholic Episcopacy. All other arguments about interpretation are simply Spackle and paint over that fundamental issue.
Seriously, do you really hope to influence Catholics to cross the Tiber by exchanging an infallible teaching source for a fallible one or is your argument only to exchange one fallible source for another fallible source? Or worse, do you expect everyone to look into their mirrors and honestly claim that in matters of faith and morals each possesses an infallible ability to interpret Scripture and that all others who differ from us is more fallible so that they alone in the universe, possess the complete Truth?
Peace be with you.