I also live locally and know the river well, having searched it thoroughly for a friend's missing dog just over a year ago. The dog went missing on a walk next to the river with no sign of him being in the water literally seconds later, however he was unfortunately found some weeks later further up stream. The river is deceiving.
I don't think it is the done thing for the police to say of anybody missing by water that they've probably gone into it, it just usually becomes apparent a little time later, unfortunately, when the water gives up the person/animal.
I don't want this to be the case, but I think it's an awful accident and time will tell.