Rendering proper 3d object into the texture uncovered another issue - framebuffer had to be cleared after switching.
Texture is still flipped :( (original scene has small red torus on the top)
This is proving to be rather tricky. Yet again I tried to handle image coordinate mess in a proper way (UNPACK_FLIP_Y_WEBGL as texture parameter and non-inverted UVs), fixing hacks across the codebase.
This did indeed help with render-to-texture flipping, but instead it created really ugly problems with both normal map and minecraft AO demos. So back to square one :(