The knee-jerk reaction to pretty much all panicky driving moments is to stand on the brakes like goblins are trying to crawl out of them, and in most cases this is absolutely correct.
That being said, imagine you’re cruising down the highway at about 65 mph when all of a sudden you hear your rear tire explode like you just ran over a tiny landmine. As you fire shit out of your pant leg like a muddy trumpet, you can feel that the car is about to go out of control. If you follow your instincts, you’ll probably hit the brakes, but in this case your instincts have tragically failed you.
See, if you brake during a blowout, you’re almost certain to fishtail (and maybe flip), possibly into another fast-moving car or the median (or both). This is especially true if your rear tire has blown out, which is more likely than a front tire blowout (front tires wear out more quickly, but people see that and replace them, while leaving the rear tires in place for years and years as part of their plan to just drive the car until it slowly disintegrates).
So in the event of a blowout, you must do the very thing that makes the least sense: hit the gas. But don’t drop an elbow on it like Macho Man Randy Savage; just squeeze it firmly for a couple of seconds to regain control, keeping the car as straight as possible. A completely blown or otherwise flat tire drags on the ground like an anchor — if you slam on the brakes, the anchor catches at 65 mph or however fast you’re going, and you’re screwed. Ditto if you smash the gas pedal, give the car just enough speed to stay in control and then gently let your foot off the gas, turning into the blown tire (if you steer the opposite direction, the anchor catches). The tire that betrayed you will eventually bring the car to a stop on its own, and then you can get out and throw your pants into the woods.