I'm sure at some point you need a pressurized suit to make breathing possible, but it likely has more to do with preventing decompression sickness and protecting against the cold (at very low pressure the moisture from your skin will rapidly boil, cooling off your skin).
The summary then would be that you aren't going to survive in a wheel well of an air craft above 35,000 without carrying both oxygen and a delivery system that is capable of maintaining an adequate partial pressure in your lungs.
Now when I visited NASA AMES during one of their many open houses we got to look at one of their U2 research planes and either I or one of my kids asked the pilot why they wore a 'spacesuit' and their response was "Because oxygen masks don't work above 35,000 feet." which, more accurately it would seem its harder and harder to make a working system as you go above 35,000'.
Very cool discussion btw, clearly its a very nuanced kind of thing.
Is there, perhaps, some reason why I can't? Lungs exploding because of the 1ATM pressure differential, for instance? It seems that 1ATM is not that much, but perhaps it is... That's what I'm curious about.