I was taught that is a Protestant notion, that Catholicism is a combination of the Bible, tradition, and Church teaching.
In isolation, yes, but he's saying that within the context of the way the Church has always understood this passage, as Our Lord teaching the necessity of the Sacrament of Baptism for salvation. It's not as if he's deciding, like the Prots, that this was some kind of metaphor for the flow of grace or something.
And what's he's saying is along the lines of what Pius IX wrote in
Singulari Quadam:
let us hold most firmly that, in accordance with Catholic teaching, there is ‘one God, one faith, one baptism’ [Eph. 4:5]; it is unlawful to proceed further in inquiry.
We know that the Sacrament of Baptism is necessary for salvation. We don't need to know or ask any more than that. This attempt to find all manner of exception, etc., serves no purpose other than to undermine this dogma.
Are the faithful required to recite back 3 pages of distinctions and explanations regarding what Our Lord REALLY meant, or does it suffice to believe that the Sacrament of Baptism is necessary for salvation, without needing to add a dozen qualifiers that end up gutting the literal sense of what Our Lord taught?
What purpose does all this speculation about a BoD serve? If God saves some souls by way of BoD, then glory be to Him. What practical difference does it make for us? On the other hand, if people start believing in BoD, it can very easily undermine faith in the necessity of Baptism. As Father Feeney stated, belief in BoD makes BoD impossible, since people replace their desire for Baptism with a desire for the desire of Baptism. We have seen its fruits, the loss of faith that there can be no salvation outside the Church. Belief in BoD has no upside, but a massive potential downside.
In fact, we've gotten to the point with the "well, we need to understand this the way the Church does" crowd that they claim that the Church has interpreted it to mean the opposite of what it actually says and that anybody who holds this teaching of Our Lord as meaning exactly what it says is a heretic. In other words, people who believe that the Sacrament of Baptism is a
sine qua non for salvation are now derided as "Feeneyite" "heretics".
So, while we have to interpret Scripture according to the Magisterium and to Tradition, the problem comes in when people "interpret" the Magisterium into explaining away dogmas. That is why we need a living Magisterium and not merely a static Tradition, since the same problem arises with "Scripture and Tradition alone" as it does for "Scripture alone".