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In the Stranger's confrontation with the town's hired guns in the bar, he grabbed a bottle in order to test their reaction. He knew who would probably draw first, who was hesitant, who was scared, and how fast they were. So when he tells them, "I'm faster than you'll ever live to be," it wasn't just bravado, it was the truth based on information that was given.
Callie's failure to injure the Stranger, despite shooting multiple times at him from less than 10 feet away, can either be chalked up to extremely bad aim or the possibility that the Stranger is not human.