It's more like a discussion start than a question.
I have seen different opinions about fishing in shallow river water. Some people said it's impossible to fish in shallow water on rivers, some people said that shallow water is wider than only this light blue part through which you can wade.
I'm going to present my own observation. If it was stated somewhere already then I'm sorry.
So, it seems that you can fish only in tiles which are at least 1 tile away from the land.
Also, shallow water is the light blue water tiles in which you can wade.
In most cases shallow water on rivers does not appear further than 1 tile from the ground, preventing fishing in it. However, sometimes there are exceptions.
An example. Let's take a look at this shore:

Here is a border between fishable and not fishable water:

And here is border between wadable and not wadable (shallow) water:

As you can see, there are 2 shallow tiles further away from the shore which ARE fishable.
When fishing in those 2 tiles I was getting different fish (including plaices, yay!) than on the other tiles.
If more people confirm this - can we put this on wiki?