I think it's more accurate to suggest that some tendencies towards sin
have their roots in our evolutionary history rather than sin itself.
Paul's writing on sin and the law in Romans 7 may tie in here. A command
had to be given and the recipient had to be able to choose between
obedience and defiance before it could be broken. Thus, the disobedience
of Adam and Eve is at the heart of human sinfulness. At the same time, sin
is ever prone to take an existing good or neutral item and turn it to evil.
An instinct for self-preservation is clearly useful for organisms, but it
is also easily perverted to selfishness; good of reproduction can be
perverted to lust, etc.
Although nature was created good, it was not without aspects in need of
work. The command to subdue and rule over the earth is before the Fall,
and I don't believe this was an insubstantial task [though it's a lot
harder afterwards]. Whether this included a mending of harm done by Satan
or simply filling a job planned in the process of creation is moot. At any
rate, "doing what comes naturally" is not necessarily good.