You almost have to assume the "max drop rate" lasted a mere fraction of a second, because the plane wouldn't just drop and then climb instantaneously. When the plan bottomed out at 400 feet, it would've been pulling up and out of the dive/descent, so the point of maximum drop rate had to have happened higher up.
Also, since it sounds like it occurred during a missed approach/aborted landing, it could've been descending anyway and the error may have only dropped the plane more/faster than it would've otherwise gone, depending where on the aborted landing the error took place. Point being, there's a lot we simply don't know from what's presented in the article (not watching the video linked, maybe it contains more details), but the article definitely uses the scariest numbers to titilate rather than inform.
Right - it's not the speed (descent rate, in this case) that kills you, it's the acceleration. 4000 ft/min is nothing in the grand scheme - that's a nice, leisurely 10-minute descent from 40,000 ft. That's well within the capability of ANY commercial (or military) aircraft out there. The potential issue is that if you're descending at 4,000 fpm, realize that you're about to hit the water, and yank back on the stick so that 0.5 seconds later you're at 0 fpm (holding steady at 400 ft), then you've put the aircraft through an acceleration (averaging) 4000 ft/min * 1 min/60 sec / 0.5 sec / (32.2 ft/sec/sec) = 4.1 G.
Now, 4Gs is not comfortable - that's in the range of the biggest, fastest roller coasters out there. But it's certainly not life threatening nor would it cause any structural issues for the aircraft. Gusts and turbulence can easily cause momentary 4G accelerations, so the structure would have been designed to handle that.
Bottom line, that rookie pilot probably just thought he saw a whale or something and wanted a closer look. What's the big deal?