Altitude sickness = Decompression Sickness?

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My error is that I thought 1 bar is 0 meters and not 10 meters. I understand now, you are correct, the snorkel idea would not work.
I think you are misunderstanding a couple different things.

At sea level, when you are at 0 feet of depth, you are under 1 bar of pressure. Every 10 meters of sea water you descend adds another bar. If you are at 5 meters, you are now at 1.5 bar--one for the atmosphere and 0.5 for the 5 meters of water.

If you dive at 16,000 feet of altitude, while you are at the surface, you are at 0.5 bar. Every 10 meters of sea water (I know, I know, it will be fresh) adds 1 bar, because water weighs the same at any altitude. So at 5 meters you will be at 1 bar--0.5 for the atmosphere and 0.5 for the 5 meters of water.
 
Just based on that article, the only treatment for altitude sickness is descent and that the bag is only used in severe cases if rapid descent is not possible. Pressure does help but not for the same reasons as in DCS treatment
 
If this is the case, why do some people get altitude sickness symptoms when flying?
The answer is in your Wikipedia article:

High altitude
At high altitude, 1,500 to 3,500 metres (4,900 to 11,500 ft), the onset of physiological effects of diminished inspiratory oxygen pressure (PiO2) includes decreased exercise performance and increased ventilation (lower arterial partial pressure of carbon dioxide- PCO2). While arterial oxygen transport may be only slightly impaired the arterial oxygen saturation, SaO2, generally stays above 90%. Altitude sickness is common between 2,400 and 4,000m because of the large number of people who ascend rapidly to these altitudes.[8]
...
Ascending slowly is the best way to avoid altitude sickness.[4] Avoiding strenuous activity such as skiing, hiking, etc. in the first 24 hours at high altitude reduces the symptoms of AMS. Alcohol and sleeping pills are respiratory depressants, and thus slow down the acclimatization process and should be avoided. Alcohol also tends to cause dehydration and exacerbates AMS. Thus, avoiding alcohol consumption in the first 24–48 hours at a higher altitude is optimal.
 
Boyan. It might help too to think of DCS as a excess nitrogen problem and altitude sickness as a reduced oxygen problem. Both are partial pressure related but otherwise very different illnesses.
 
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