Nope, the partial pressure of O2 (what matters to us humans) does infact drop as you ascend. Water vapour changes in inspired air is not relevant to respiratory physiology calculations because you can safely assume the air in your alveolae is 100% saturated at any altitude you are likely to find yourself at.
Got a few spare minutes to edited to provide some figures.
Sea level. Partial Pressure 02 = 760mmHg * 20% (approx O2 concentration) = 152mmHg
6000ft. Partial Pressure O2 = 609mmHg * 20% = 122 mmHg
8000ft. Partial Pressure O2 = 564mmHg * 20% = 112mmHg
Therefore at 6000 cabin altitude there is indeed 20% less O2 in the air available to us humans, and (as this is not PC to say and I take the risk of having my account terminated
) the journo is correct!
Due to the marvellous and elegant design of the haemoglobin molecule humans can compensate for this extremely effectively and blood O2 levels for a healthy individual will remain safe. There will always be borderline humans where this increase in cabin altitude will cause them distress.
If you want some more figures and graphs showing how haemoglobin affects things then go
to the USAF Flight Surgeon Guide