Regarding your last statement, many, MANY very smart people have believed this to be true. The concept of the fall of man and the restoration through Christ is front and center in scripture. The book of Romans goes through this very logically, clearly, and methodically (though is certainly not the only scripture to deal with these ideas). No great thinker who has accepted Christiantiy has accepted it without accepting the concepts of sin that we are talking about.

Simply put, here is Christian belief about sin and death:
1. When man was originally created, it was in a sinless state in which there was no death. Humans would not get old and die, nor would they die for any reason. They were created to be in a perfect love relationship with God forever.
2. Man was given a choice to choose self over God, and this choice man did make. The result was that sin entered the world and creation fell. People got old, sick, and died. Violence entered into the world, not as part of God's original intent, but as a result of man's sin.
3. Every human since Adam has followed in his footsteps, commiting sin and earning death. We could perhaps assume that if someone were to live a sinless life they would not die, but no man has, or can, achive this, as we all partake in our spiritual heritage of sin (Jesus would have been the exception, in fact, except that he chose to give his life in exchange for ours). As you say, we cannot correct this because we are all, in the final analysis, selfish beings that choose ourselves over God.
4. We are lost in physical and spiritual death because of our sin, destined to remain separated from God forever. We have no hope of overcoming sin and defeating death because all have chosen emnity with God.
5. Jesus lived a sinless life (He is God and was able to achive what fallen man could not) and offered himself as atonement for sin.
6. As a result of sin, man must still experience physical death, but spiritual death is overcome through the redemptive work of Christ. Those who accept the atonment of Christ will live forever in a love relationship with God.

This is about as core to Christianity as it gets- the central theme of the Bible is man's fall through Adam and the restoration through Christ.