Earlier quoted context omitted.
In America you can sue anyone for anything at any time. Whether you will win or not is another matter, but if you've never been to jury duty the court system is absolutely packed with cases that seem absurd. In this instance, it would be perfectly plausible to sue for something like emotional distress.
There is no way a lawsuit like this would survive a motion to dismiss. Intentional infliction of emotional distress requires an underlying wrongdoing, among other things. There was no legal wrong committed when the document was leaked.
[1] https://www.justia.com/trials-litigation/docs/caci/1600/1600...