One note about that video: he's updated his advice a bit. Our shitty Supreme Court has made "stay silent" a bit of an issue--it's safer to demand your lawyer instead.
It's not even about understanding the system, the presence of the lawyer forces the police to establish "scope".
If I'm just a witness, then the lawyer can make sure that what I say can't later be used against me for something unrelated.
If I'm a suspect, this prevents the police from going on a fishing expedition to just "find anything". Once they talk to the lawyer, they have to go hunting for "what they told the lawyer" as opposed to everything in the world.