LE knows how close the river is and they seem to have known from the beginning who did it. I suspect they have been working since day one on building a "can't recover the body" case.
And, for what it's worth, I suspect that they have a whole lot of evidence they are building their case on.
Which is also why the lawyers are gonna do all they can to keep their clients quiet now. You are not allowed to lie to the police, and any lie, any inconsistency in the story -- coupled, for example, with HRD dog hits and some forensics, could be enough to send them to prison forever.