When I was in LA Co as an EMT, I was told in class that there were only 2 authorized painful stimuli...the nail bed press, and the pen-between-the-knuckles squeeze. I do remember being told in class specifically not to do sternum rubs...I also remember someone saying that was at least partially due people doing it wrong, that the running was more likely to cause skin damage and that the real 'proper' way was more of a roll, pressing your knuckles into the sternum vs a rub.
That all being said, as best I can tell, that's all pure anecdote. I don't think I've ever seen any official "this is a proper way to do a sternum rub; this is the improper way" nor do I remember an actual specific protocol in LA Co specifically saying which specific painful stimuli were and were not authorized (though it is LA Co....I wouldn't be that surprised if there was one buried in there that I had missed....not being in LA Co anymore, I can't be assed to look that up right now lol). In real world practice I felt like I was the only one who ever did the nail bed pinch, most every one else did a trap squeeze or the sternum rub anyway, never heard of anyone getting in trouble for that, or that they shouldn't do that.
In my current National Registry EMT class (part of my fire academy) I will say our instructors specifically said trap squeeze was the preferred method, though that just may be the local preference...and FWIW they also showed the sternum rub and made no mention on it not being allowed, and I personally used the sternum rub on the mannequins for skills testing and had no problems with that.
