Just checked the docs again, and you're right, it does say "The texture rect is useful when you don't want to display the whole texture, but rather a part of it. By default, the texture rect covers the entire texture."
I first found out about setTextureRect in the shapes tutorial. Pasted from the section about texturing shapes:
"Shapes can also be textured, just like sprites. To specify a part of the texture to be mapped to the shape, you must use the setTextureRect function. It takes the texture rectangle to map to the bounding rectangle of the shape. This method doesn't offer maximum flexibility, but it is much easier to use than individually setting the texture coordinates of each point of the shape."
This is what had me confused: nowhere in the tutorial did it say that the default is to cover the entire section. Nor does it use a code example that does not use setTextureRect. I suppose if I had read it again I may have noticed that the language does sort of imply that setTextureRect is only necessary if you want to display a portion, but only if I had reason to believe so already. From what it said, I thought that setTextureRect was a mandatory function used to position the texture on the sf::Shape. I am sure that I am not the only one who was confused by this from the tutorial.