The innateness of personality is obvious in kids because they haven't yet had the time to undergo any meaningful environment-induced (or self-induced) change. They express their raw nature.
However, I believe that experience shapes personality significantly over the long term, especially between the ages of ~15 and ~25. I also believe that people are capable of deliberately building themselves, choosing to alter their own personalities through a wide range of means. The person you were born as doesn't have to be the person you die as.
We have multiple reasons for wanting to believe nurture is more important than nature and none for wanting to believe the opposite (unless we = the far right, which we ≠), so it's not surprising we overestimate its effect. But man are kids' personalities inborn.