I haven't been able to hook it up to a real amp yet (moving houses) but I'm going to pull out the tube amp tomorrow to test the hum since my test rig for pedals/builds is a 10 watt starter amp that buzzes anyways.
From memory the buzzing dropped out a bit when I flicked to middle and got louder on neck/bridge positions. This wasn't normal hum though - definitely sounded like a ground issue somewhere.