They are way too well trained to fall for this prank. If they were able to confuse driving and flying like this they should be on sick leave immediately.
Yeah, my first thought as well was that "pulling up" would be pulling the steering wheel back, which wouldn't do anything. Certainly wouldn't swerve the car all the way off the road, you wouldn't want to jerk a plane left or right in that scenario either.
So... definitely made up. But still an amusing greentext.
Also, yanking back on the yoke as hard as you can when you hear a terrain alert is a pretty surefire way to crash and die anyways. So yeah, fake and potentially gay.