Gavra – no contradiction. The moral code to which you refer as being ‘overidden’ by the Torah can and does exist naturally in society but the point is that they cannot be described truly as ‘good’ or ‘bad’ as these terms have NO TRUE MEANING AT ALL unless there is a G-d given Law – the Torah – that provides the ultimate definition of right and wrong.
Without the Torah Chas V’Shalom, Human Society and its interactions, a moral code with its laws and behaviour is coldly reduced to the following:
1)A bunch of atoms grouped together in a certain way (the Human Form)
2)These atom bunches are capable of interacting within themselves in a particular way (Thought and Choice).
3)This often results in a further External interaction with other similar groups of atoms in various ways (e.g. providing them with “food” which prolongs the time they exhibit the property known as “Life” or, the opposite; e.g. putting a sharp knife in them thereby removing from them the property known as “Life”).
4)Many of these bunches of atoms have collectively over the years internally interacted resulting in something known as a “Decision” that some External interactions shall be named as ‘good’ and some ‘bad’ in accordance with the ‘Feeling’ (another property exhibited by these atoms) that these external interactions foster.