He definitely shouldn't have mentioned the guy's wife and kids, but it's certainly not against the law. It's definitely not bright to admit in public to hacking computers in the same way it's not bright to admit in public to doing drugs, but it isn't actually against any law but the law of prudence and good sense.
I think I missed something. How did he hack the other guy's computer? He based his analysis on email headers received in his own computer, and used Google, whois, fb, etc. after that. Right?