Looks like everyone is trying to "get a piece of the action". I remember NTSB investigators criticizing Asian and Eastern European authorities for opening criminal cases after crashes. Greg Feith, the One and Only, has said it many times (may be a misquote): "As soon as there is a threat of jail time, people start hiding things instead of helping to find the cause of the crash".
While punishing those who are responsible may be important, a much more crucial task is make sure it never happens again. And that's where FBI investigation may become an obstacle. It also puts different laws (and lawyers) in motion. People may start hiding behind warrants, injunctions, court orders, etc. I wish any criminal investigations would stay away until NTSB and BEA have done their jobs.