The particulars of that case matter though.

In this case, the suspect had spoken to the police, and during this didn't respond to a certain question / responded to the question with silence. If I recall correctly, the court reasoned that by first speaking, he gave up his right to remain silent. Moreover, he responded by silence rather that actively asserting his right to remain silent.

Not to say I agree with the ruling, especially because he was never mirandized. However, it is not clear cut that simply remaining silent isn't enough to assert your right against self-incrimination.

Many years ago, in New Zealand, the flatmate of a friend of mine told me much the same: if you're questioned by the police, you can't just stop talking and claim your right to silence. You gave that up by answering questions.