In light of history this appears to great advice. I always remember that some of the biggest gangsters, mobsters and crooks were not put away for their crimes. The got away with boot legging, drug running, book making, murder, extortion, bribery and theft. What put most of them away is simple stuff like tax evasion. They didn't report and pay tax on the income the law new about, and they got them.
When people ask me what to say when talking to a grieving family I always tell them that most of what you say is meaningless and stupid. Grab their hand or hug them, say "I'm sorry," and SHUT UP. Same goes when the cops come - SHUT UP, and don't say a word until YOUR attorney asks you to tell HIM your story.