No no, I meant the preamp section of the integrated. It has a feature that let's you bypass the preamp section and use the output control on the DAC instead. When I did this, the hum came back. I don't know what that means, but you're right, the issue must reside with this particular amp because I've never had a hum otherwise.
That sounds like a problem with the DAC. So if the amplifier is using its internal preamp, no hum, but if you connect the DAC to one of the inputs and use the preamp section's volume control- you have a hum (or buzz), right?
If yes it suggests an issue with the DAC. Since you did something to it as suggested in the posts above, it might be that there's more to it than a missing shoulder washer.