Not to pick nits, but he doesn't mean that the battery is connected across the 120VAC line, but rather that one of the terminals might possibly be referenced to the AC line.

Had it happen just yesterday - we were at a customer troubleshooting our 90VDC motor equipped product running on a third-party motor controller. I was measuring the encoder feedback signals with the customer's brand new four channel o-scope. I was hesitant to connect the probe ground lead to the negative side of the 5V encoder supply. They assured me that the encoder supply was isolated from the AC line or at least at referenced to ground. I threw the switch and ZAP-POW and smoke wafted off the board. Luckily it burnt the "ground" trace off the motor control PCB rather than blowing the scope. Turns out the encoder supply was referenced to the +380VDC bus on the board which was referenced to the AC line which was referenced to the same ground as the scope.