Catholics probably do say something like that but isn't it " ..... people choose to go there by rejecting JESUS ......" After all, the idea is to accept JESUS, pray to JESUS but not to God. But I think the main theme is that you have a chance on your death bed or even your in last breath to ask JESUS into your heart and it's considered being a Christian. Am I right?
In Catholic teaching, God, Jesus, Holy Spirit are one. We do pray to God...to Jesus...to the Holy Spirit. Jesus is sometimes easier, because he did become man, but even then prayers are through Jesus and through the Holy Spirit. God the Father Creator who created through the Word (Jesus) and the Holy Spirit hovered over all. The Word became man and sent the Holy Spirit (New Creation and Word) into the hearts of mankind. (Something like that, because as we are often reminded we can finish emptying the ocean one seashell at a time before we can even begin to understand Trinity.)
As far as deathbed Christians: That is up to God who knows the heart. Jesus taught repentance meaning turning away from sin and instead doing the will of God. Obviously, if someone is dying they can no longer actively sin any more than they can do the will of God in place of that sin. Still, Jesus taught, "Sins are forgiven" so there is that hope. If someone has a good, sincere heart, then that person walked into the vineyard at the last hour, and Jesus told the story that those who walked in at the last hour had the same reward as those who entered at dawn.
I also keep in mind that saying that to God one day is like a thousand years; a thousand years are like a day. That is a lot of time for the Lord to work.