This isn't so complicated. Tiger simply cannot speak to the police because if he tells them the truth, it will be released to the media and everyone will know that money can't buy your way out of a Jerry Springer relationship.
On the other hand, if he gets caught in a lie about what happened, he could be charged with giving false statements to the police and everyone will know that money can't buy your way out of a Judge Judy show, not to mention the $100M per year he makes in endorsements.
I'll take 'Tiger Banging the Skank' for $1000, Alex.