I know we all can't say how we would or would not act in a situation but what I think could have avoided that whole thing is if the driver of the initial horse turned him straight into the wall. He was obviously trying to stop the horse at first by pulling on the reigns. When that didnt work, where did he go? Did he fall out or did he bail?
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The guy got tossed out, so he couldn't really do anything. And honestly, if he had bailed, I wouldn't blame him. It is absolutely terrifying to have a horse take off like that and have no control over it. When they are spooked and scared like that, you can't do much to control them. Especially when they start rearing.
At the track, there have been numerous horses caught by someone stepping out in front of them, and grabbing the lines (not reins), and no doubt at driving competitions as well. You catch the head, you catch the horse.