Eclipse: sorry but it's nonsense. in 3d space there isn't something like a texture -> screen resolution correlation because the 3d object are moving and rendered with different perspection. if you ever played DooM you know that at every resolution you play if you get close to a wall pixels are 100 times bigger than the on-screen pixels.
Naturally, any texture will pixellate if you zoom in far enough. The reason it's so obvious in Doom is that it uses extremely lo-res textures, so that even in the smallest resolutions, the wall textures pixellate. Such were the limitations of the hardware back then. There was no 3D acceleration, and the game had to be able to run with no more than 4MB of RAM. This put sharp limitations on texture sizes, both because they had to fit into a very small memory space, and because there was not a lot of processing power available for rendering.
Eclipse: Texture resolution and screen resolution matches only for HUD elements.
Look again at PhoenixWright's screenshot. The HUD elements are heavily pixellated too.
And the texture resolution doesn't have to match the screen resolution, unless the texture takes up the entire screen. It just has to be big enough not to pixellate at the size you will normally see it at. Again, if you stick your face in the wall, the wall texture will pixellate no matter what you do, but then it's not meant to be seen that close.