OP apparently managed to clear up the mistake without much bother by speaking to them (although they were understandably shaken up by the experience). This presumably wouldn't have happened if they'd done what you suggest.
Not speaking to law enforcement outside the presence of your attorney is excellent advice. There's no downside to having the attorney there, and potentially life shattering downsides to attempt otherwise.
OP apparently managed to clear up the mistake without much bother by speaking to them (although they were understandably shaken up by the experience). This presumably wouldn't have happened if they'd done what you suggest.