it's 512x512 actually. The thing that you have described with uv stretching is caused by attempting to squeze your screen resolution to that square space. If you have 16:9 screen ratio, then you will have to adjust in same manner your uvmap. That also means, there is no reliable way to have PiP behaving on all screen resolutions/rations. Most extreme thing happens with triple screen setup.   Sort of workaround is using UVAnimations but I haven't tested it yet