Windows Integrated and the domain name

Windows Integrated authentication works great, but when it fails (because the user doesn't have the site in the intranet sites for example) they are prompted for credentials. Unfortunatly, instead of defaulting to DOMAIN\ it is COMPPUTER\ and of course that never works.

Why in the world would you want this domain based service to default to the local machine SAM? Anyway, how can I set the default to be DOMAIN\ when the user does not provide the domain information?

This seems like a silly default setting to me.

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