O2 monitors that you see clipped on to people's fingers or toes are saturation monitors, they measure how saturated the blood (hemoglobin, actually) is. That is, what percentage of hemoglobin molecules are carrying as much O2 as they can. So it can't be above 100%.
PO2 monitors on a rebreather measure the partial pressure of O2 in the loop. This is the product of the percentage of O2 in the gas (FiO2) and the ambient pressure in atmospheres. That's different from saturation.
The monitors that I show at the end of the video aren't saturation monitors. The one on the rebreather is measuring PPO2, and the one on the anesthesia machine is measuring FiO2. They are the same at sea level. I don't know what would happen if you took an anesthesia machine underwater, but I suspect it would void the warranty.
While theoretically you could measure O2 saturation during a dive, I don't think that would be helpful, since you could become hypoxic and lose consciousness before the sat monitor could react. The anesthesiologists in this threat (paging
@rsingler ) can probably answer that better, as far as how tightly linked those two things are.
You can definitely see desaturation even if the PPO2 is high enough. We see SAO2 drop pretty rapidly in infants if respiration is obstructed, but that has to do with special considerations (functional residual capacity, etc..). And people with lung disease (e.g. pneumonia) will have an increased A-a gradient, which means that they might desaturate even if they are breathing supplemental O2.
The thing is that it's fairly easy to measure PPO2 in the gas, and if that's in normal range, then no need to measure SAO2 since those other physiological things aren't going to really change during a dive (maybe immersion pulmonary edema would increase your A-a gradient, but I don't see rebreathers being designed to monitor for that). Of course, that depends on the PPO2 measuring device working correctly, and a lot of rebreather training is about that...
