You can render a 1x1 texture in 1080p, but that doesn't take up all that much space. The information needed to render at high resolutions is rather small.
The textures themselves are just images. You know how you take a picture with a camera and it takes ~4MB, Well, I can render that picture at whatever resolution I want (it may not turn out so great) but it still takes ~4MB. The best way to reduce my download size wouldn't be to change the resolution I render that 4MB pic at, but to reduce the size of the picture to 2MB. The quality might drop, but the resolution it is rendered at will stay the same.
EDIT: there is a difference between resolution rendered at, and the resolution of the textures themselves. I am under the impression that the reference above is to the rendering resolution.
