What the statement I put above conveys is a few things.
1. That I respect the cops and their job and that I know they aren't after me personally(and hence won't try to parse every sentence I say and take it out of context like you did)
2. That I've been told by people that I believe to be knowledgeable that even innocent people can be convicted of a crime they didn't commit by saying something stupid and that's the reason I have a choice in not talking to them (and hence putting the "stupid" burden on my by implying "I don't think I'm smart enough to be in a discussion with you")
3. I explicitly stated "I'm not guilty" letting the cops know I'm not trying to be smug with them and that I do want them to know I'm not guilty.
Bottom Line: By saying "No Comment" you're trying to prove you're smarter than the cops while my statement lets them think they're smarter than me while still giving them nothing they can use against me