By definition, you can't be one by accident. Its a mindset where you actively -look- for ways to maximize your potential and minimize your weaknesses. Its a lot like criminal law - in order for you to be guilty of something, you need both the criminal act, and the criminal mind set. Killing someone is not a crime if you don't intend on killing someone.The point is that apparently people can become a "min-maxer" by accident as it is rather easy to create very powerful characters just by following guidelines, rolling well and taking a thematically relevant feat.
In this case, the lack of intention is what makes it not be a min-max. As I've said its a mind set and style of play. I personally just think you're mistaking a min-maxer for someone that happens to have a strong character. The two are not synonymous.