Exactly. If one of us said, "When in the course of human events", people would take it as an allusion to the Declaration of Independence. If we said that in the context of a government abuse or usurpation, it would be taken to have a clear and unambiguous meaning. Quoting the first line of Psalm 22 is no different.
The Church has never made Herself judge over the souls of men. That is Christ's alone and it is His prerogative to welcome us home. The Church teaches us how to live and worship in the Family of God. Those who come to repentance without a chance to enter the Church may experience a "Baptism of Desire" where they would have been baptized had there been time. Certainly, if you follow Jesus's ministry, had their conversation occurred not on the Cross, Baptism would have followed.
I am here explaining Church teaching on a specific subject. I carefully consider all of my responses. Where I am wrong, I have admitted it. I claim no infallibility. I haven't criticized every response on this thread because many have been correct. I simply answer where an answer is needed.