Just because you have the "right" to not incriminate yourself is not the same as saying "dont' talk to the police". If no one ever talked to the police, that is when our system is broken.
The original point was why did he not talk to the police at his home in Florida - my opinion is that he didn't want them to notice he was wounded, scratched up, and didn't want to reveal his guilt by talking like he did in Utah. He was talkative in Utah. Not at all in Florida.
Gabby was not his possession. She was a person with rights herself - rights he took away - and someone's daughter, and sister, and granddaughter. It was not BL's right to hide what happened to her just because he felt like "Constitutional rights" should be exercised for the heck of it.
JMO