I just completed a deep dive of the press conference on this thread, and have skimmed most of the rest of the posts. My reading is that:
a. The dog has gone down towards the steep part leading to the river bank, and behaved in a way so as to cause the missing person to panic.
b. In this situation, getting the dog out of perceived trouble has been more important than any teams call, and the phone may have fallen to the ground.
c. The MP (sorry I wish to distance myself rather than pretend to be familiar) has slipped or lost footing when trying to help the dog, potentially sustaining an injury.
d. Realising the predicament, the MP has released the dog from the harness which may have been on, and thrown it back towards the path - or the dog has grabbed the harness and taken it down towards the river in a hopeless attempt to re-engage the owner.
e. MP has done best to swim, with the current of the river, at some point has gotten out of the river, or has remained in the water.
f. Hypothermia has resulted from the cold.
g. With great regret, I conclude that either unconsciousness has resulted and the MP has been carried further than expected, or has exited the river at some point much further than expected, and succumbed to hypothermia.
h. In the best case, the MP is surviving but severely impaired or injured. If hypothermia set in due to the cold, it would be extremely difficult in the circumstances to recover core body temperature.
There are obviously alternative hypotheses, but this is the one that came to mind. I sincerely hope that the MP is found as soon as possible.