It's a good rule but in extreme cases I'm sure it can go either way such as free-divers who can hold their breath for five to ten minutes when diving but the world record is 22 minutes (when not diving).
That's because as you descend, the partial pressure of oxygen increases. You require somewhere north of 0.10 Pa02 for consciousness; at sea level you have 0.21 Pa02. So you can consume enough oxygen at depth that when you rise you grey or black out; it's common enough that if you take a breath-hold diving course they will train you to 1 - know how it occurs; 2 - dive in pairs (always one up, one down); and 3 - make sure you are weighted so that your body is buoyant by 20 ft or so.
Also when under pressure the spleen shrinks substantially which raises the level of oxygen-enriched hemoglobin.
I've read plasma gets squished out of your blood and fills body cavities such as sinuses to keep your head from imploding.
there's also a reflex which causes your hearth rate and breathing to slow if you feel cold water on your face.