It's got to get to court first and if you stay silent then it means the police have to build a case without you assisting them in it. No one's going to stroll in and say "I did it". If you were innocent you'd happily give all the information you could. But plenty get done for crimes they didn't commit because they talked and the police felt they had enough to prosecute with. There was that bloke recently who got done for rape when he had a solid alibi and looked nothing like the image of the man the victim had described to police, had no previous. The police didn't bother looking into another guy with a background who was known to be in the area.
As you say, in court if I was on the jury I'd be convinced of their guilt on the basis they didn't talk and then took the time to sort a story out!