If you haven't read Dev's post on this issue, stop what you're doing right now and get on it. It's much more thoughtfully-expressed than what I have been stewing over!
I just wanted to share some reflections on the topic. For reference you may want to read Allie's post which brought this all up... especially the comments afterwards.
The welcome thing: we only have an informal, rarely-discussed, unnamed thing like this, and it only comes out when a spaz does something unacceptable.
For example: I got a massive neck stinger from a whitebelt guy jamming my head into the wall (he launched forward with me on his back, about 18" from the wall, with my arms trapped in a seatbelt grip) once... a couple min later, one of our smooth, polished (bigger, male) purples asked him to roll. He elegantly, methodically tapped the guy with one sub per joint, top to bottom, down one side and then the other, within about 6 min. No exertion, just looked like a nice flow roll. It was so professionally done that I didn't even realize till later that it was the unspoken way our school looks out for its own... especially its own girls, smaller people, older people, etc. And of course I learned that if my head had been in the proper position, I wouldn't have been injured by his forward roll, so that was good to learn.
But as far as routinely attacking and "humbling" people when they walk in, no way.
As for the norm in terms of popping stubborn tappers.. I can only tell you what I have personally heard of and experienced.
I have trained at 4 different schools in California (Ralph Gracie Berkeley (Eduardo Fraga), Bay Jiu Jitsu (Stephan Goyne), 10th PJJ SF (Denny Prokopos) and New Breed (Johnny Ramirez, Cristian, John Ouano, Val Worthington)), tons of schools in Texas and have discussed this issue with people all over the US and the world, including (in the last several weeks) Thailand, Ireland, England, France, Mexico, India, China, and Paraguay.
I have NEVER heard anyone, ever advocate that stubborn tappers should be popped whilst training.
Maybe I'm overdramatizing it but I don't think so. You might think that "just an elbow pop" is no biggie, but I'd rather roll with control and pass on a tap than stop someone from training for even a week. Why not? What's the advantage to me of forcing them to tap? Isn't the WHOLE POINT OF TAPPING the AVOIDANCE OF INJURY!? Geez oh pete-- hurting someone to make them tap so they don't get hurt is like hitting a kid to show them you don't hit.
I know that you love this like I love this (if you're reading this blog I bet I'm right!) and that to take time off, whether a couple days for a popped elbow or 6 months off for ACL surgery, would really hack us off, especially if we thought we got popped too hard, too soon (and wouldn't we all, for the most part?)
And for me, closer to home: Leila's neck is amazingly good considering it was broken less than a month ago. She was LUCKY. If the (bigger, stronger) whitebelt guy had been going fractionally harder or faster, who knows what would have happened to her spinal cord. And they weren't doing anything terribly scary-- "it was just a stack pass." If our academy permitted people to roll like it was a fight, to "test" themselves... she could be a paraplegic from C5 down. Or dead.
It is our explicit policy to "train today so you can train tomorrow" (not "next week after you ice it" dammit) (not "If this were a fight, how quickly could I end the match? Tap him. Go hard. If he doesn't tap, pop his elbow") that makes me comfortable rolling with almost anyone at my school, once I see they've been there long enough to lose spazhood status. If my instructor's explicit advice to me was anything otherwise, I would bolt through the door and never return.
And this whitebelts/heelhooks thing. Ahem.
You're going to be doing jiu jitsu for years! YOU DO NOT NEED TO LEARN HOW TO ESCAPE AND PERFORM EVERY SUBMISSION IN YOUR FIRST TWO YEARS. Leave the more dangerous ones for later.
Sorry for shouting. Just had to get that off my chest.
Edit: Here's Allie's great follow-up post.