
They don't care about Tiger or his career. They only want to peek, poke and prod into his private life, examining rumors that the accident was the result of some sort of inappropriate or salcious behavior. Any traffic defense attorney who is worth a rat's ass would tell him to make no statement whatsoever to the police or the press. Every single word he says can and will be used against him. The cops aren't his friends, they're getting paid for trying to pin charges against any and every person they can.
If the police charge him with something that doesn't include jail time or license suspension, his lawyer may advise him just to pay the fine, especially if he wouldn't even have to appear in court. And if he is charged, his own statements will eventually be scrutinized with a microscope in the press, and therefore by the prosecutors. So he would benefit by keeping quiet and preserving the advantage of trial by surprise.
Largely thanks to the "DUI exception to the Constitution", the traffic laws are now so heavily enforced and basic trial rights are so minimally observed that the defense has very few advantages. Best to make maximum use of one, which is the right to remain silent. The critics? What does Tiger have to prove to them?