When I claim that you can "hold your breath for 4 minutes" after deep and rapid hyperventilation, I mean that CO2 levels will NOT rise high enough to warn you before hypoxic blackout (if you hyperventilate for long enough beforehand). So, I'm not denying the possibility that you pass out at minute 3 or 4 (which TECHNICALLY means you aren't holding your breath for the full 4 minutes), but this is actually just what you want. Again, you do rapid and deep hyperventilation for maybe 3 minutes, then you exhale as much air as you possibly can, and then (while still holding your breath) securing the bag over your head and tightening it so that there's almost no air in the bag (and no airflow). However, your criticism isn't valid for what I'm describing, because the reason people sometimes wake up from unconsciousness (after doing hyperventilation + breath hold) is BECAUSE there is a source of air to breathe (which contains oxygen). I'm saying that if you drastically limit the amount of air in the bag, you limit the amount of oxygen as a consequence. Now, how do you know if it is too much air? That is a more complex question that is quite reasonable, but again I'm just explaining the science as it is. Now, if you can find me an example of someone doing something actually similar to what I'm suggesting, I'd love to look at it.
Edit: just to be extra extra clear about what I'm suggesting, here it is:
1. Hyperventilate (rapid and deep inhale and exhale) for maybe 3 minutes or once you start to feel intense tingling (your hand might even want to close into the shape of a lobster claw, caused by extremely low CO2 which is what you want)
2. As soon as you're done with the hyperventilation, IMMEDIATELY exhale as much air as possible (not to the degree that it causes a lot of discomfort, but the more the better)
3. As soon as you have exhaled all the air, DO NOT take another breath in. The next steps require you to hold your breath (with minimal air in your lungs)
4. Secure a small-ish bag over your head and tighten it so that it is as snug as it can be around your head (this is EXTREMELY important), and make sure that it is so tight that air CANNOT get in.
5. Continue to hold your breath, and eventually you should pass out from hypoxia. At some point, your unconscious body will make extreme attempts to take air in (convulsions), but there will be SO LITTLE air (and as a consequence, so little oxygen) that you will continue to be unconscious until you die.