That is true, and the majority of the church since Augustine v. Pelagius has been aligned with Augustine, the theological champion of original sin or as it is also known, moral inability (to please God in our natural condition.) Pelagius, and pelagianism were declared heretic and heresy.
The “sour grapes” passages you referenced do not, in my opinion, come anywhere close to refuting the doctrine of original sin. In a proof-text battle (which I detest) the original-sin [1] side wins hands-donw, in my opinion.
[1] I speak of original sin in the sense that we each inherited a fatally defective morality from Adam, not that we are charged with Adam’s sin as if we committed it.