I understand, but those things are not the reasons Catholicism does not recognize Prot. denominations as Churches. The Orthodox don't exactly like our formulation of those ideas either (BTW 3 is still very up for debate and I particularly don't like it very much), and yet they are considered proper Churches.
Where the rubber meets the road is, as jude24 very astutely said above, sacramental theology. Catholics believe that the sacraments were instituted by Christ to dispense grace among the faithful. The Church is where the sacraments are. Where they do not exist in their true fulness, there cannot be the Church.
When you good folks hear us say that though, (and please correct me if I am mistaken), you hear that phrase as a total denial that you are Christian at all. Because you view the Church as an invisible institution solely of those who have believed in Christ.
It is very important for non-Catholics to view this document in terms of *our own* ecclesiology, and not any one else's. We go by the sacraments, not just a sinner's prayer. And note well that we recognize one of your sacraments (Baptism) as valid...so we are forced to recognize that there is some element of the Church among you, even if the other sacraments are not.
Claud, where the rubber meets the road is Jesus saying that those who worship must worship in Spirit and in Truth.
Those who teach obvious, made-up UNTRUTH cannot be the true Church, no matter if they’ve got sacramental theology coming out their ears, complete with real-life, true splinters from the actual Golgotha cross itself and the factual, actual Holy Grail to drink from.
Human lineage is of no importance. Props are of no importance. SPIRITUAL, TRUTHFUL worship is what matters. The RC FLUNKS the test with a number of things, the most egregious being: assumption, immaculate conception, and coredemption of Mary.
For all his vaunted, entirely too opulent status, Pope Benedict is an empty vessl, “pontificating” foolishness, traditions of men, and UNTRUTH.