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It's not 'false' at all.
I know there are various ways to tell, by the bobber being still in a pond, and moving in a river, and obviously any water leading directly to the mouth is river and not pond, but unbroken waterfalls turn ponds into rivers.
I've even got a large section I made in my cemetery that is half pond, and half river, with a waterfall on one side.
I make these things all the time, and there was even a way to make a trash spawning pond, that had to do with the size, shape, and direction of the fall, but I believe that may have been patched.
In my experience, a waterfall has always turned my ponds into river (fish) spawning ponds.