Full screen quad texture coordinates mapping
I may have misunderstood, but it sounds like the frame buffer you're rendering to is only 2×2 pixels? In that case, the fragment shader will be evaluated at each pixel center, which will be at 0.25 and 0.75 in UV space. So with a threshold of 0.95 you will indeed not get any pixels green.

If you use a larger framebuffer, say 100×100, then the last 5 pixels of each row should come out green.