I've seen that video somewhere else a year or three ago. Although aimed at the US market it also applies to most of the civilised world.
I worked quite some time in the military justice world, dealing with minor stuff like traffic offences as well as criminal matters. In all that time and having read thousands of voluntary statements there was only one which got the accused off the hook, in that case it was a speeding offence. It was his estranged wife who had run off with the car and judging by the photo it was definitely not him, unless he had a serious hormone problem. Most of the time people not only failed to exonerate themselves, they sank themselves even deeper in the brown and smelly, that included one bloke who was from the Army Prosecuting Service!
Don't talk to the police also means don't make written statements.
And don't talk to the police.