Your argument would be like saying the Democrats are Constitutionalists. After all, the Constitution was written by those who would join the Democratic-Republican party. But to equate modern Democrats with the founders of the Constitution would be a mistake because it neglects two factors: firstly, that the Democratic-Republicans underwent a split in the 1850's to form the Democratic Party and the Republican party, and secondly, that the Democrats don't stand for the same things the Founders did (limited government, etc.)
Now, how do we know that that isn't the case with the Catholic church? That, over 2,000 years, their theology has evolved to get away from the apostolic teachings demonstrated in the New Testament, and that a closer representation of Christianity isn't found in the Orthodox or Reformed branches of Christianity?
(Incidentally, I'm trying to not bash... so please don't take offense in my comparing the Catholic church to the Democrats. I mean nothing by it other than an illustration.)