I've also raised this with BBC News. Just because someone is a polar explorer does not make them an expert on what should be done.
Paramount is safety, which means "don masks, get the plane down to a safe FL, then talk the passengers through what just happened".
As for "there was NO warning, it just happened" - Well matey, that's what's called an emergency.
And I do agree with what others said - If you'd listened to the safety briefing, you would know that the bag does not inflate, but that the oxygen does flow if you pulled "the mask sharply to your face" as so many briefings clearly point out.
BBC News just published an article that explains some of this:
BBC NEWS | UK | What to do when planes lose pressure
S.