That's the whole point of not talking unless a lawyer is present (and you give them a chance to vet your speech). You have very little chance of knowing what is incriminating, and this is by design.

Their job is to put away criminals. In the case where there is not really a crime, their training, which is meant to get confessions from actual criminals, ends up pulling seeming confessions to nonexistent crimes from innocent people. After that happens, you are screwed.

Even in cases of "actual" crime, the system is quite content to put away innocents.

Note that even denials, e.g., "I have no idea of what you're talking about", can result in charges, if they're provably false (e.g., there's a record you do know what they're talking about -- email, twitter, writings, conversations, etc.). These typically lead to various "obstruction" charges.

Simply refuse to comment.

Don't say anything. At all. Nothing you say will help your circumstances, but it can hurt you.

Actually, according to the supreme court, you have to verbally invoke your right to remain silent. If you dont, and they harass you for 16 hours and you say anything, its fair game. If you do, and they opt to keep harassing you, its not.

I know what you are getting at, but that recent SCOTUS decision didn't implicitly say that. However, it did make it clear that you can't talk with police (thus waiving your right), refuse to answer a question, and then answer other questions. In essence, it's not the police's job to figure out whether or not you're invoking your right.