Hrms... I believe script kiddie is someone who only downloads a program and clicks some buttons in order to 'hack' a server (they actually have no idea what vunrabilities they are exploiting). A white hat is someone who has ALOT of technical knowledge and usually knows how to program and discover their own exploits without using securityfocus.

With that said, I would say the administrator who uses SK programs to test his/her own server is not a white hat or a script kiddie. They are just an administrator testing their server. It requires next to no knowledge to use a SK program, and just because someone is a system admin it doesn't mean they are automatically a white hat.