If you have Tableau Server you can publish the data source as a live connection to Tableau Server and allow the users to connect to the published data source but prevent them from seeing the credentials.
More information can be found in the Online Help guide: Data Security
Hope this helps!
We found that TS connects to databases using its network account and not a run as user account (that's just the way we setup our server), so using your logic you could give your tableau server network account permissions to access your database, although your security team will be screaming at you as this is really-really bad practice.
Depends on how secure you need your database to be