We don't believe we bear the guilt of Adam and Eve's sin as if it were our personal sin. Although it is proper to each individual, original sin does not have the charecter of a personal fault in any of Adam's descendants. It is a deprivation of original holiness and justcie, but human nature has not been totally corrupt...Baptism, by imparting the life of Christ's grace, erases original sin and turns man back toward God, but the consequences for nature, weakened and inclined to evil, persist in man and summon him to spiritual battle. (CCC 405)
The Council of Trent is merely balancing the heresy of Pelagianism, which calls Adam's sin a "bad example" and that men of today are not effected by it vs. the Protestant Reformation, which claimed that man was radically perverted and had NO freedom of will. The Church refutes both positions.
"By one man's disobedience many (that is, all men) were made sinners"..."sin came into the world through one man and death through sin, and so death spread to all men because all men sinned" (Romans 5:23, 19) Since the whole human race is in Adam "as one body of one man (as we are in the New Adam)", ALL men are implicated in Adam's sin and ALL men are implicated in Christ's Justice. While we do not have personal guilt, we, as one Body, share in the guilt of Adam. Since Adam received original holiness for himself and ALL human nature, his fallen state is also propagated to us. Original sin is a sin "contracted" not "committed" - it is a state, not an act.
Regards
Interesting read on Augustine here:
http://www.goarch.org/en/ourfaith/articles/article8153.asp
You're quote from Romans is hardly explicit to indicate the concept of inherited sin as opposed to inherited will to rebel against God (sin). The Orthodox church reject the doctrine of original sin and the filioque of Saint Augustine. The Bishop of Rome holds to this doctrine.