Here's an interesting story from Skybrary about a Boeing 737 that was given an altitude below the Minimum Vectoring Altitude. I fly in mountainous terrain, so this is a particularly important topic.
The 73 got a "Pull Up!" warning from whatever terrain system they had. It was an -800, so presumably they had some kind of visual terrain warning available (my $700 Garmin handheld and my FlightGuide EFB and my SkyCharts EFB all provide this). Did they not monitor the terrain?
And what if this had been on a cold day? With an airport elevation of 639', an aircraft indicating 7800' on a -20C day is more than 800' lower; this airplane passed less than 700' above the terrain.
And it has happened to me, more than once. "Cleared as filed, maintain 9,000" didn't make any sense with 12,000' terrain so close, so I asked. Whoops! I wasn't cleared as filed, I was cleared on a victor airway that went the other way, over lower terrain.
The pilot (or crew) is always responsible for terrain clearance. Always! Use all the tools you have.