2002 Ford Focus

Car run great all day. At night came back from work and parked temporary some distance from my spot. Run upstairs to drop some stuff and came back to repark the car by reversing it into my spot about 40-50 ft. Engine started fine. On start, the radio, heater were on and since it was a short distance I did not turn my lights on. I backed into my spot but wasn't satisfied with the angle. Moved forward, put it back in reverse and at this point I turn on the lights while I was moving in reverse. The engine had an electric shutdown and stopped. It was electrical because the radio reset. I immediately cranked the engine and started fine. I moved into my spot, stopped the engine and waited a minute or two. Restarted the engine and again no problem. Drove around for 10-15 minutes with no problems. So I am concluding that the battery was fully charged all the time. If it wasn't the car wouldn't have started the first time. The battery is less than a year old and if it was charged then the alternator must be at least charging the battery fine. Since the car was moving when the shut down occurred it must be the alternator. But what is it? An internal short? Regulator? And can it be diagnosed beyond of what just happened? And can I have a bad alternator and still have a healthy engine start? No warning light (dimming or flickering). Technician at the dealer had diagnosed an overcharging alternator 1 year ago. Since then I discovered that the battery was the wrong kind and dismissed that diagnosis after replacing the battery and constantly checking for overcharging. And if it is a bad alternator and needs replacement that's fine, but I am concerned that maybe the engine belt that drives the alternator is somehow malfunctioning. Is that even possible?