Looking at the Boeing electrical schematics for the 737 (Ref 49-62-11), I see that there are several 28v dc inputs going into the APU controller. If the APU fire handle is pulled, a 28vdc signal is sent to the APUC. If a fire is detected, a 28vdc signal is sent to the APUC. If the APU is switched off, a 28vdc signal is sent to the APUC. If the battery switch is switched off, 28vdc is sent to the APUC. Presumably all these 28vdc signals are shutdown commands.
In the latter example, the signal goes through an air/ground relay ("R38" on the particular schematic I have). The contacts of the relay are opened in the air, so the "battery off" shutdown signal cannot get to the APU.
This explains the how. I'm still not sure of the why. All that battery circuit seems to be doing is providing you with less ways to switch off the APU in the air.
Rgds.
Q.