Hehe, I got it wrong again. (Boy, I need to learn to shut up when I don't kow what I am talking about.
)
Most of the jet's thrust is produced by combustion of the air after it's compressed. If the compression alone was producing the thrust basically it would just be an inside out propeller.
So the answer is, yes it's the lack of oxygen required to burn the jet fuel efficently that makes a jet engine not be able to operate efficently at extremely high altitudes.
I found a preetty good link to refresh up on jet engine principles if you are interested.
http://www.soton.ac.uk/~genesis/Leve...h/Jetprinc.htm