I have no explanation to offer, but I'm curious and have a question.
Have you tried using capacitance (~20kuF) between the battery and the amp? I found that the battery with capacitance and switching supply (alone) to be indistinguishable. I never used the battery alone to see if it made a difference. I think I used a Nemic Lambda 12V, 2 or 3 amp switching suppy for the comparison.
Edit: I did hear a tiny bit of noise from the switching supply with high efficiency speakers...I still use batteries.