After Salinas v Texas, you must positively assert that you are exercising your right to silence, not simply remain silent.
The prosecutor in a murder trial argued, at trial, that silence of the defendant (during police questioning) was evidence of his guilt. The supreme court in Salinas v Texas allowed this.
* The defendant also selectively answered some questions, so perhaps there is nuance, but to be safe, a positive assertion of right to remain silent seems prudent.
IANAL, and would love if an actual lawyer would comment on this.
The police have a lot more power in any encounter, and there is no way to avoid having them make your life worse. About the only truly concrete advice is that if you are guilty of something then you absolutely, positively must get a lawyer before saying anything at all. The magic words are “I will not answer any questions without my lawyer present,” and any variation from that exposes you to the risk of the police creatively misinterpreting you.
The magic words can help you beat the rap, but they cannot help you beat the ride. If they decide that you are going to jail, then you go with them, and nothing you say or do (or not say or do) will prevent that. And you will stay there until your lawyer shows up.
Also, don't take my word for it - here's a US police officer saying the same thing: https://www.youtube.com/watch?v=d-7o9xYp7eE (skip to the second half)
He wouldn't talk to police.
This is addressed explicitly and at length in the video linked in TFA.