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Turbocharged vehicles lose power at altitude for various reasons.
A turbo doesn't care about psi. It only cares about pressure ratio. If you are at sea level (14.7psi ambient) and want to produce 14.7psi boost, the turbo workload is 2.0 pressure ratio. Right now, my altimeter watch is indicating 12.02psi ambient. For the same turbo to produce 14.7psi boost, the turbo workload is 2.22 pressure ratio ((ambient+boost) / (ambient). It is working harder to produce the same PSI.
The problem is that when turbos go higher and higher in the pressure ratio metric, they produce less additional PSI and more heat. Hot air = bad.
To compound the problem, the intercooler is less efficient. At altitude, there are less molecules moving across the intercooler fins. It is therefore less efficient at drawing heat away from the intake charge.
Some cars (Sti, I believe) have ECUs that are tuned to reduce boost at altitude. That reduces the stress on the turbo by making it work at the same pressure ratio.
BMW will up boost to compensate for lower ambients. However, it does not fully compensate. That implies to me that in stock form, the turbo has enough headroom to spin faster and compensate, to an extent, for the thinner air.
Throw in a tune and the turbo is working incredibly hard at altitude.
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