This explains the AC coupling, but not the coupling to 50% of VCC rather than to GND.
Normally if GND is grounded, such connection would put 50% of VCC ripple on the case. Usually a cap is placed between the case and GND alone.
But this is a floating circuit, so maybe they figured that its average potential is constant and equal to the midpoint between BAT- and BAT+, hence such grounding.