It might be that Plinius is using an additional circuit to convert from balanced to single-ended. This is a common practice (not one I'm in love with...). If the opamp associated with the conversion has gone noisy, that would certainly explain why you don't hear the noise on the RCA input.
Does it do it without the cables attached (no input, but set to balanced)?
Does it do it without the cables attached (no input, but set to balanced)?