Making a false statement to a police officer is itself something they can jail you for.
The best thing you can do when a cop seeks to engage you in a discussion (and he's not your buddy discussing football), is to say "My lawyer's number is xxx-xxx-xxxx, please discuss it with him", and have that be your reply to everything he says from that point on. Except if the question is "may I come in?" or "may we discuss this inside?", where your answer is "No"
You make a good point of law. Knowing one's rights and how to exercise them is if utmost importance. Of course in my personal case the only guns they might have any paper on have been sold so if they are specific I can honestly say I don't own them. The bottom line with the law comes down to what they can prove but honesty is always the best policy and silence is often the best defense.
When a cop visits you, it is NEVER because he wants to talk about football. Before inviting him into your home, always ask what it is about, and ask if there is any reason you cannot discuss it outside. If he says he HAS to come inside, that is a good sign it is serious and you already need a lawyer. If a cop stops and helps you on the street, he is your friend. When he comes to your home, he usually ain’t your friend, and you should not start out thinking he is.