Incorrect, for the reasons the video linked numerous times throughout this stated. By proclaiming your innocence, even if true, you could be found liable for an increased sentence for lying to an officer if dodgy evidence incorrectly 'proves' you guilty later down the track. This exact circumstance is covered.
Your 1 and only word is always 'lawyer'. Nothing else.
Your 1 and only word is always 'lawyer'. Nothing else.