You got it. This is the Church teaching: Christ converts some whose hearts are open to the Truth, to His one Church, on their deathbed. Thus a righteous Muslim dies Catholic. There is no salvation outside the Church.
Except that you cannot be righteous by works... it takes faith, which comes by hearing, hearing by the word of God. Faith in Christ and his substitutionary atonement.
I dunno... I'll keep an ear open, but I don't like ecumenicism... I would never want us all to pretend to agree... just for the sake of getting along. (this is different from getting along in spite of not agreeing, which I do think is valuable).