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.