Both Adam and Eve sinned. Eve listened to the serpent and ignored what God had said to Adam. Adam despite knowing what God had said, listened to Eve. So they both sinned. It seems that they did indeed have a natural tendency to sin, since they both sinned by disobeying God's command.Whoa now . . .
Adam and Eve were not created with the natural tendency to sin. When God said that all that He had created was "good," He might as well have said "perfect."
Adam and Eve were born with one Nature . . . the Human Nature. The purpose of this Nature is to serve, and this Nature will serve whichever Spiritual Father it belongs to, be it either the Devil or God, the Father. Humans serve, and that's it.
When Adam and Eve sinned, their disobedience caused their eyes to be "opened" to sin, but closed to God. Thus, the Purpose of Christ is to redeem us from the Curse/s that came from Adam and Eve's unholy work. Jesus accomplishes His Purpose through His Holy Work, which is to Circumcise hearts of this Sinful Nature, He also grants the ability to Repent, He also grants the Holy Spirit, and belief in His death and resurrection along with believing in the Power that raised Him from the dead . . . these are His Holy Works. These completed Works of Christ result in the Effect of Christ, which is a Transformed human being. Any person who once possessed Satan as their Spiritual Father, and is then adopted by Christ as their Spiritual Father, there is a colossal Transformation and it is unavoidable.
When Adam and Eve sinned, their eyes were "opened to sin" by eating from the tree of the knowledge of good and evil. They had the choice not to do so. Why did they sin and disobey God? Because it was in their sin nature.
Genesis 3:6-7, "So when the woman saw that a) the tree was good for food and b) that it was a delight to the eyes and that c) the tree was to be desired to make one wise, she took of its fruit and ate, and she also gave some to her husband, who was with her, and c) he ate. Then the eyes of both were opened, and they knew that they were naked, and they sewed fig leaves together and made loincloths for themselves." (my additional notations, of course).
She saw that the tree was good -- a serious misjudgment. She saw that it was a delight to her eyes -- another serious misjudgment. She thought that the tree would make her wise -- another serious misjudgment, the opposite of faith. And Adam , who heard directly from God, ate some of the fruit anyway. He disobeyed God's command. So they both sinned. Why? Because it was in their nature to sin. Why else would they have sinned???
I agree totally with your last paragraph.