Yes, because no charges had been filed against Beth to begin with. There was therefore no double jeopardy in play at all.

The thing about this episode that doesn't hold up internally is that the recollection of shots first and then the alarm should have been learned the night of the shooting and not held back for the "gotcha" clue at the end. To me it's always been the episode's biggest flaw.

Yes, I agree. If something that shocking happened, I would think that in reality that character would have replayed the events over in his mind multiple times and connected the fact that the gunshot was what triggered his reason for immediate notice, not any alarm. That always seemed weak to me as well, but the episode was good nonetheless.