Chris Scott:
If the APU battery took no significant part in the APU start, it seems an odd coincidence that the failure should have taken place so soon after APU start, at the end of a 12-hour flight.
For whatever reason, the battery was still being charged a rate of ~45 amps 15 minutes after the APU start. Since there should be no other loads in flight (unless the BOS plane had the same cross-wiring problem as the other), we can safely assume that it at least contributed to the APU starting current.