well, i guess if you shoot someone, i do hope you get tricked into admitting it...
the rest of the criminal "justice" system is bullshit, but i do prefer to separate murderers from other people...
....
regarding never admitting something, sometimes it actually works in your favor... especially, or only really, if you're directly caught.
lying to a cop will piss them off, and is technically another crime. apologizing will often get you you a warning...
(the 5th means you don't have to incriminate yourself, but doesn't give you permission to lie)
especially if you look chagrined and throw a "sir" in there...
source: lifelong petty criminal
p.s. you can kinda combine the two with "oh did i? i'm sorry... i thought i came to a full stop..." and then fight it in court.