The problem is that they would have to prove that Bloomberg wasn't just incompetent, but rather malicious. It's entirely possible (and imo the most likely scenario) that Bloomberg didn't fabricate the story, but were duped.

This rarely works. And it's not the company that would lead such a lawsuit, it's the shareholders.

That's not true. The company would have plenty of damages to their reputation that a lawsuit would be perfectly reasonable. Not to mention the fact that lost market cap also damages the companies ability to hire and retain talent.