SQL Trusted Connection runs with the permissions of the local machine, not those of the user. This isn't very useful when connecting to remote machines. Even if the user is a member of the Domain Administrators group no privileges will be granted by the trusted connection (e.g. to create a database) because it's running with the permissions of the machine account, not the user.
In http://www.advancedinstaller.com/forums ... php?t=1915 an Advanced Installer user complains about an error "Login failed for user 'DOMAIN\USER$" and wonders where the $ is coming from. The $ indicates that this is a machine account, which happens to be identical to the name of the user.