I agree, it's called a felony stop.
You make commands (with another officer if at all possible) from your vehicle. You tell them to turn off the car, then put their hands out of the window, then open the door from the outside leaving their hands out of the window so you can view them. Once they are out make sure they are facing away, then you tell them to take their right hand while keeping the other up and pull up on their shirt collar and turn slowly. This allows the cop to see if anything is in their waist line under the shirt or else where. Once the cop is satisfied there is nothing there, you tell them to slowly walk back towards you keeping their hands in the air, walking backwards. You tell them to stop in front of your car and get on their knees (camera should always be there and on). Then you tell them to put their right hand on the ground followed by the left, then walk their hands forwards until they are prone. Or you can tell them to cross their ankles while they are on their knees keeping their hands in the air. Then you tell them in either position to interlace their fingers behind their back. This is where the other officer comes into play more, they cover as you handcuff then search. Notice I said tell them, not ask them. You have to tell them and be authoritative.
That is how you do a stop where you suspect someone has a gun and committed a robbery. You don't just go bebopping up to the window and do business. If it turns out you have the wrong guy, you explain to them the situation and apologize to them for their inconvenience. You explain that they matched a description of a dangerous person who committed a serious crime recently in the area. Hopefully they understand, if not then oh well.
If it turns out to be true that the vehicle he was in had a matching tag from the crime that cops were looking for, it changes things a bit. If it turns out that the woman lied, that also changes things somewhat. The Sheriff stated that he did not have a carry permit from them, maybe he had one from another city or bordering state. Maybe not. What doesn't change is that in my opinion if the cop suspected that he was the one from the crime that they were looking for, he should have handled it very differently. If he had done like I explained, there is a very high probability nobody would have been hurt.