You are, of course, correct.
Without a doubt, the guys who leave people face down in arroyos in Mexico are visibly impressed by the Majesty of The Rule of Law in El Estados Unidos de los Estupidos, and are about to renounce their lives of horrific crime this very day.
Undoubtedly.
Right after they get finished laughing their murdering butts off at seeing one of their hit men put two American cops in the slammer for the forseeable future.
Are you arguing that police should be allowed to shoot anybody they pull over, if those people run away, so long as when we finally investigate the people it turns out they are illegal aliens or have committed a crime?
I would note that being an illegal alien is not a capital offense, nor is drug smuggling, but shooting a person could well kill them.
Would you be OK if these agents had shot you in the back, so long as they "thought" you were an illegal alien who was drug smuggling and you had a gun?
Oh, of course, you would never run away from a police officer. Of course, a police officer would never try to hit you with their weapon when you were surrendering either.
Why don't we just agree that the whole situation is preventable by building a high voltage electric fence/virtual fence with moats on either side stocked with hungry barracudas.