I'm a newbie, having followed this story from the start.
I'm leaning towards her having fallen in the river, as it seems the most simple explanation. There is one thing that others me though. I can totally get on board with the cold shock scenario but if you fell into the river, even a tumble down the bank at speed, you wouldn't end up far from the bank at all. Looking at the pictures of the police in the river, that area wasn't deep at all. If you fall in water fully clothed with two layers of padded coat/gilet, they won't become water logged immediately (most coats have a minimal amount of water resistance) you would have a few seconds to right yourself and potentially stand up or take a layer off.
Also, the padding of the coat and gilet would protect your body from the initial cold, the water wouldn't get to your torso until it had waterlogged all the layers, again giving you time to stand, shout, scramble out.