So, the actual criteria is is breathing. I'm throwing "pulse" in there because there's no way an ER doc isn't going to check for one.

You're absolutely right that finding a pulse can be tricky (though a carotid or femoral is a lot easier than a radial). There are a handful of good studies that show a fairly high degree of uncertainty, even among well trained providers (ER docs, paramedics, etc). This is why breathing is the "real" criteria, and should have been the decision making criteria used in this case.

Thanks for clarifying -- that makes more sense. Is it possible that casualties were arriving too fast for him to confirm that they had good airways? I have no idea how long that takes.

The goal is to take ~20 seconds. You position the head and neck in a position where the airway would be open (if someone is unconscious, they can't maintain their own airway, even if it would otherwise be fine). After positioning, take 10-15 seconds to observe for breathing. During this time you might as well check for a carotid pulse as well.

The article says that he triaged 150 patients in 30-40 minutes, or one every 12-16 seconds(!!!), so it sounds like not spending the 20 seconds it would take to check for breathing may have been the right call?

Some of them would have been a lot quicker than that, some would have taken a bit longer. In studies the mean is generally in the 15-20 second range, but some individual data points are just a couple seconds and some are >30 seconds.