How do you know the flooding you are about to wade through to save somebody is not electrified with a current not made by water?

I would think if the wires are live, they would be giving off sparks.  That should raise a red flag.  A couple of people were electrocuted trying to rescue some folks.

You cannot, fallen power wires do and will happen. But:

A) Distance is a super isolator, a fallen wire 200 yards away is pretty sure to have found other places to ground itself long before it even think of grounding through you.
B) "Waders", those hiphigh boots sports fishermen use, are very good insulators and will protect you from even high voltages in the water. Even if you dip your fingers in the water there will be nowhere for the current to go to. You will be like all those birds you see, sitting happily on active power lines.

The water would act rather like a Faraday cage and earthing-point combined, so no current will flow through you. Further, I'd have thought the cables breaking and dropping into flood-water would cause massive earth faults that would trigger the distribution circuit-breakers to isolate them pretty well instantly.