Yeh you'd have to eat a stupid amount of acid/shrooms to die directly from the drug, shrooms is something like 19.6g of pure psilocybin to die, which equates to a FUCKLOAD of shrooms, even this is supposed to be lower than the actual amount needed to kill a human and it only takes about 20+mg for a powerful trip.
LSD is the same aswell taking about 80-240 tabs (dependant on the potency) would theoretically lead to death, but again this number is supposed to be much lower than the actual dosage required.
And where did you hear about the only reason you trip is because oxygen gets cut off from the brain??? Have you got a link for that? cuz if its true thats sum scary shit