Are you testing localstart.asp? I have to check to confirm, but I don't think SafariDriver starts up on that page as the default when you launch SafariDriver.
I can't help you here. Maybe someone else can.
Here's one thought: if you are testing localstart.asp, it could be that opening that page from SafariDriver (e.g. consider it like opening via Javascript code) is treated by Safari as a security risk and hence you may get that and not when you browse there normally. And/or the Safari session started by SafariDriver is not associated to your Windows account login, and hence you are prompted for login, whereas manually using Safari is attached to your Windows account (which may then auto supply your login implicitly), this is particularly true if your localhost web server is IIS using Windows authentication.