From the previous thread:
Scary thought: even the truth doesn't necessarily help you when you are under investigation for a crime.
Calliope posted this video some time ago:
http://www.youtube.com/watch?v=i8z7NC5sgik
On Youtube, it's called "Don't Talk to the Police" but it could equally well be titled "Don't Talk. Period."
In that video, Professor James Dugan gives a hypothetical example to illustrate why talking to the police is a bad idea, even if you know you are factually innocent. The relevant bit starts at about 21:30 but the entire video is well worth a watch.
His example runs something like this: say the police are interviewing you about a hold up committed in your town. You know you didn't do it and you can prove it: you were at your mother's house which is located five hours away. You tell the police this.
Then the police find a witness who knew you from high school. This witness is telling what they believe to be the absolute truth: that they saw you two blocks from the scene of the crime only an hour before the crime was committed.
Now your credibility has been impeached. The police believe that you lied about being five hours away and who is going to believe your own mother when she says you were with her that evening? The spotlight instantly turns on you and, well, in that situation bad things can happen.
Professor Dugan says repeatedly in that video that you cannot help yourself by talking to the police, you can only harm yourself. By extrapolation, I'd say the same thing is true of giving media interviews. It's fair to assume that LE would go over anything she said in public with a fine tooth comb.