Ive been getting this problem on my AMD 5870 card for a couple of driver releases now (at least since 11.9), the recent 12.2 drivers dont seem to change much.
I have an OpenGL FBO with an attached depth/stencil texture, and two color texture rectangle. I then attach and share the depth/stencil texture from the first FBO with another FBO, which itself has another four texture rectangles attached, this is for a deferred rendering setup.
Once the scene is drawn and lighting is blended in on the second FBO, with the depth/stencil and a single color texture active, I forward render some blended quads (shaders off), when quads intersect with the existing world it produces a checker pattern not seen on my other non amd card. See attached image.