something is not quite clear here. If the amplifier has the volume all the way down, no sound ought to come from the inputs. It MUST be in the amplifier stage(s) following the volume control. Typically a circuit is switches --> volume --> preamp line stage --> power amp/current amp.
So i suspect this is not electronics hiss at all, but some kind of high frequency interference that comes from whatever device (Denefrips????) is connected. Note i have Denefrips and it is very, very quiet. It is also isolated at its USB input. That said i also isolate my bridge and power them independently.