Sounds like they took off into a descending airmass that was descending faster than they could climb. Scary, but I think such a mass of air will flatten out and spread as it gets down near the surface, allowing you to fly out of it and climb. It might be an issue if there were obstructions in your path, but unlikely to push a plane into the ocean.
The media is portraying this as a “nose dive” which is annoying, since it definitely wasn’t that.