Per the teardowns, the non POE units use simply 12v PSUs inside for those models. What I'm curious about is if the POE voltage drops, if the switch handles that ok (both firmware and physically).Well... how could you run those switches with an internal PSU with just 12V? Via the PSU#2 power socket at the back?
Oh, don't try to hook it up to an ATX PSU. The connector is the same but the voltages don't match, you'll end up damaging the board.