I believe that DIR-Atlanta is confusing two things.
Bungee = shock cord. Enough said.
What he is speaking of when it comes to breaking is actually surgical tubing. Surgical tubing != bungee.
So far I can see perfectly acceptable ways to attach your backup reg (in no particular order):
1. Bungee that uses the slipknot method
2. Bungee that is held in place under the zip-tie on the mouthpiece
3. Surgical tubing held in place under the zip-tie
Now, let's think about this logically. To me, they all make sense--just use whichever. I know that many people recommend using bungee under the zip-tie because it "won't come out when snagged" and it "won't break", but in all seriousness, how long is it going to take before you have to worry about breakage for the surgical tubing? A year, perhaps? If it's that long, then just replace the darn thing! Surgical tubing is cheap, as are zip-ties. If you go that long without inspecting your gear to check for things like cracking hoses or leaks, then there are other issues at hand...
As to using the bungee slip-knotted--this is what I personally use. The only drawback (especially for me) is that sometimes I'm just plain stupid and forget to grab it while walking out the door. I use mine both at school helping out with classes and also out in open water, thus it gets moved back and forth. The simple solution to this is to make multiple octo-necklaces, which I just recently did. We have backups of backups of everything else, might as well have a few spare octo-necklaces on hand too.
As to the issue of having the slipknotted version come off the reg--if you have it nice and tight on the mouthpiece you'd have to work pretty hard to make it come off. Even if you DO manage to get it off, big deal. Hopefully everyone learned regulator retrievals in their basic OW class and we should all be relaxed/calm enough in the water to find it. If it isn't hanging under you then it's probably behind you, which means you might have to grab the first stage, ok the hose, and find the reg. If you can't find it then your buddy should be there to help. Personally I've never had any issues with mind coming out of a nice tight slipknot but I can't speak for everyone.
As to having the shock cord under the zip-tie, that sounds like a nice way to do it as well. Keeps your octo-necklace where it should be and it probably won't break.
Just pick one and make sure you know why you picked it. To be honest, any of them will probably work just fine.