When you are picked up by LE for a crime, it is not a court of law. While you do not have to "prove you are innocent" to them, it is in your best interest to do so. It is different than "proving you are innocent" in a court of law at trial. Something which we know you do no have to do, although if you can it certainly can't hurt your case. Your rights in the criminal justice system should not be a consideration when first picked up by LE for a crime you didn't commit. Your innocence and immediate freedom should be. If you can prove it and go home the same evening, you will.
And what if you can't prove it but you know you are innocent. In a great many circumstances its in your best interest to shut your trap if you are picked up by the police even if you are innocent. You really need to watch this video, it comes in two parts:
https://www.youtube.com/watch?v=i8z7NC5sgik
https://www.youtube.com/watch?v=08fZQWjDVKE
Part 1 is a law school professor. Part 2 is a cop. Both explain why you should never talk to the police even if you know you are innocent. Granted this video discusses things in the United States but I would think the same principles apply to the Canadian legal system.
In Part 1, listen to these points regarding a client who knows they are innocent:
"3. Even if your client is innocent and denies his guilt and mostly tells the truth, he can easily get carried away and tell some little lie or make some little mistake that will hang him."
"4. Even if your client is innocent and only tells the truth, he will ALWAYS give the police some information that can be used to help convict him."
"5. Even if your client is innocent and only tells the truth and does not tell the police anything incriminating, there is still a grave chance that his answers can be used to crucify him if the police don't recall his testimony with 100% accuracy."
"6. Even if your client is innocent and only tells the truth and does not tell the police anything incriminating and his statement is videotaped, his answers can be used to crucify him if the police don't recall the questions with 100% accuracy."
"7. Even if your client is innocent and only tells the truth and does not tell the police anything incriminating and the entire interview is videotaped, his answers can still be used to crucify him if the police have ANY evidence, even mistaken or unreliable evidence, showing any of his statements are false."
At 16:00 of Part 1, there is a quote which is extremely telling:
"One of the Fifth Amendment's basic functions is to protect innocent men who otherwise might be ensnared by ambiguous circumstances. Truthful responses of an innocent witness, as well as those of a wrongdoer, may provide the government with incriminating evidence from the speaker's own mouth."
Food for thought.
Now, I think based on the evidence we've heard of thus far that DM had a direct link to the demise of TB. But make no mistake, that right to remain silent is there to protect innocent people from wrongful conviction.