The phrase you used, "more pressure", can be broken down into two aspects: more horsepower and more detonation. I'll describe those two and then list a few other good ways to kill a turbo motor:

#1 - More boost with enough fuel creates more horsepower; too much horsepower and you'll snap a rod and/or crankshaft.

#2 - More boost without enough fuel creates knock, and knock is the precursor to detonation. Detonation (pre-ignition, the combustion of fuel & air inside a cylinder before the spark plug fires) causes insanly high cylinder pressures well beyond what a normal boosted cylinder would endure. This is a very powerful force and can snap bottom end components though typically you'll see a blown headgasket first. It's not usually horsepower that blows headgaskets but detonation instead.

#3 - The third way I can think of to detonate is to have very very hot incoming air, possibly due to the turbo is too small for the application or maybe there's a slightly undersized turbo no intercooler. If the air coming in is too hot it will have a much greater chance of detonating regardless of how much fuel you throw at it.

There's a fine line to be found in tuning. Richer (more fuel) is safer to a certain degree, but it also means less power. Go too rich and you start knocking due to there being an excessive amount of fuel in the combustion mixture. Leaner (less fuel) equals more power up to a certain point, but after that knock appears which then creates less horsepower. Higher exhaust gas temperatures is a side effect of leaner tunes.

The trick is to tune very well. Everyone says "that motor will take 8 psi" or "don't boost over 6 psi", but that's not it: every motor has a horsepower limit, not a boost limit. Average turbo owners don't tune well and as a result they can detonate, hence people believe they can only run 'X' psi. If you have access to the proper equipment you can tune a motor for no knock and maximum power.

#4 - Some people ignore knock and lean the motor out too far causing incredibly high exhaust gas temperatures, sometimes in excess of 1800*F. Temperatures like these can melt valves and do serious internal damage to the motor.

These are the four ways I can think of to kill a turbocharged motor at 1am on a Saturday.