If if he was stealing sh!t, you don't track him down and shoot him.
Do you assume they started off or intended to shoot him at any point prior to him turning into the shotgun?
Because other than that there are lots of people out there who might choose to follow/cut him off in order to (lawfully) detain him while waiting for the cops to arrive. At gunpoint, even. A former cop would be well aware of the lawfulness of that.
Once the fight breaks out all bets are off. If they have the wrong guy then they're instantly farked. And to be sure, the 20/20 on this guy is that he didn't have a significant criminal history or a pattern for burglary so at this point "wrong guy" is more likely than not. OTOH, there's apparently a home security video out there of one of the burglaries in progress as well as an eyewitness who saw someone at that construction site and made the phone call, so these can absolutely be compared for their similarities or their differences to the victim.
Moreover, the facts about whether or not these guys actually picked an innocent man are already known and have been known from the outset. But have not yet been released by the cops/DA or reported in the press. I don't think it's unreasonable to wonder why this is.