The father of one such servicemember, Albert Snyder, apparently got upset enough to sue for invasion of privacy and intentional infliction of emotional distress. Somewhat to my surprise (I'm glad, mind you, but a little surprised), he won, and won pretty big. Jury awarded $2.9 million in compensatory damages and $8 million in punitives.
Mind you, of course, there's no way he's going to GET that much money - for one thing, these nutjobs don't HAVE $11 million. Be interesting to see if he can keep his win on appeal, though. Much a fan as I am of the First Amendment, just this once I hope he does.