Your GPS enabled flight computer will indeed yell at you VERY LOUDLY if you're about to hit a mountain. It will not allow you to get particularly close to terrain without noticing.
"TOO LOW – TERRAIN" vwoop vwoop
You say GPS-enabled. What about a GPS-jammed flight computer? Can that do it too?
I'm wondering what they could have done differently here. The report said it was a 0% moonlight night, extremely dark. No exact position from GPS, and visuals on the landing strip. That mountain peak would have likely been invisible from the pilot's seat.
What would have been the "skill issue" difference people keep mentioning? It's getting really frustrating how reckless the US military is with the skies. They keep putting people in danger. I can't help but think about the DCA crash due to the continuity of government drills.
There's no reason they should have been flying dark for a drill that night.