The wording of the family and how LE is treating the investigation does make it seem like they think she's no longer alive. I wonder if they've gotten any clues in that regard, or they're just being realistic based on the situation.

Not a knock, but I would expect LE to have a bit more urgency if they expected she was still alive ... the investigation drawing on for over a week with few clues makes it seem very grim.
Of course, that being said, I do hope there's a chance she's still alive

Heartbreaking situation all around.