Belt stops spinning while engine is running, problem fixed itself?

Exactly what’s in the title, last night my cars belt stopped spinning while I was sitting in the parking lot with the engine on idle, I heard and felt a thud and the battery icon came on, so I immediately thought it was the alternator. Popped the hood and sure enough the belt had stopped spinning, but the engine continued to run; I shut it off and talked to a buddy and he came out and wanted to see if it started so he could see the problem. I started the car and sure enough the belt starts spinning again and the alternator begins charging the battery again. I decided to take the car to a shop and told the mechanic my problem, he said he’s never heard of that and told me it was nearly impossible since the belt is keyed to the crankshaft and should spin regardless. We tried to recreate the problem but to no avail the belt continued to spin. He checked the tensioner and the balancer, and everything looked good, he told me he had no clue how that could’ve happened, and I honestly don’t think he even believed me. This has only happened onc. I personally think maybe it’s the air conditioning causing it to lock up. I wanted to hear your thoughts because I have no clue how this could’ve happened and really don’t get how it just fixed itself?