Correct. I was pondering on how the sin nature is passed on, whether genetically, by nurture or by some spiritual means. If it was exclusively a genetic transfer from Adam then it seems it would require the fall to take place before Adam and Eve conceived which, IMO, would only be a few days at most. If it was only passed through genetics then Eve would not have had Adam's sin sature but a sin nature of her own, but still the same sin nature.
Thinking of this I also considered Jesus, not having a sin nature, since he did not come from an earthly father. This seems to further support the idea that the transfer of the sin nature is at least genetic and currently only via the spermatozoa that fertilizes the egg. Since Jesus was not affected by the genetic transferrance of the sin nature and since He could not commit sin, he could not obtain a sin nature through personal transgression and therefore he was able to be without a sin nature throughout his life.