You have the shorthand summary of Christianity, and not a very good one. On the other hand, "Everyone is responsible for himself" is the better shorthand summary.
It is an astonishing story. Jesus announced he was from God and had a message, a new Covenant/Testament. Repentance for the forgiveness of sins! The Kingdom of God is within the reach of all of mankind.
If someone were to come to you today and say, "I have a message to you from God," how would you react? Right! The same with people in Jesus' day. They reminded Jesus a Covenant with God had always been marked with a blood sacrifice, and how were they to know Jesus wasn't making the whole thing up. Jesus responded, Look at the good works I am doing, works that could not be done without the power of God behind them.
The Temple authorities of that time blew him off and advised him to cease and desist. Jesus was adamant he was doing the work of God, and he would remain obedient to his mission. So he was put to death, and ironically, his critics now had their blood sacrifice for a New Covenant/Testament. The Way of Redemption was indeed open as the Father had promised, and one could choose to pursue salvation (with fear and trembling was how Paul put it).
The Good Thief who was hanging beside Jesus on a cross as well had compassion towards Jesus when so many others (including the other thief) were mocking him. He asked Jesus to remember him when he came into his kingdom, and Jesus responded, "This day you will be with me in paradise." In this thief we see the change of heart (repentance). He reached out to Jesus and his ways (redemption) and salvation followed.
The story of the Good Thief is the exception of a life turning on a dime. It is not the general rule as the lives of the Apostles will attest--as the lives of the many followers of Christ will attest. Christ did his part of assuring all of Redemption, that sins are forgiven, and the Way of Salvation is open to all. As you say, that choice is where everyone is responsible for himself.