There's hundreds of reasons you might easily fall into the river, the simplest are trip on something (pothole, rock etc), Stumble over the dog or whilst playing with it, lose balance while picking something up, slip on damp grass. There are steep banks which would be easy to fall down, hard to get out of, and easy to hurt yourself falling down.
I can't get my head around people finding it so hard to believe its even likely.
I understand exploring the idea that someone else is involved, but to say that her falling in the river is far fetched, over leaving the field with no evidence, leaving the dog, lead and phone behind. Which one is more far fetched?