I think the flaw in the debreather approach, and the reason you don't lose consciousness within a few breaths with a debreather, may relate to the fact that there is about 1 litre of oxygen stored in the red blood cells in the bloodstream. Plus there is another litre of residual oxygen in the lungs, even when you fully exhale. So the body normally has 2 litres of oxygen stored. Given you only use about a quarter litre of oxygen per minute, that two litres will keep you going for a few minutes, even when you oxygen supply is cut off.
When you use the inert gas method, that stored oxygen I think may be passed out of the lungs, and is then expelled from the exit bag placed over your head. This may be why you lose consciousness within a few breaths with the inert gas method.
But with the debreather method, if the stored oxygen is passed out of the lungs, it will go into the debreather's air bag, and then get breathed in again. So therefore it takes longer to reach unconsciousness with the debreather, as the oxygen gets recycled, and it will take a few minutes to use up this stored oxygen. More info in
this post.