That you're reading back in rendered pixels and strongly depend on their mathematical exactness/reproducability sounds like a design flaw. What's the purpose of this action? If you, for example, need to extract some information from the image, why don't you try to extract this information from the abstract, vectorized information prior to rendering?
Anyhow, if you depend on external rendering code and there's no way to make your reading code more robust to small errors, you're signing up for lots of pain and maintenance work. Other people could break your code with every tiny patch, because that kind of pixel exactness to the bit-level is usually a non-issue when they're doing their unit tests etc. Let alone the infinite permutations of hard- and software layers that are possible, and all might have influence on the exact pixel bits.
If you only need those two operatios: lines (with different widths and colors) and quads (with/without texture), I recommend writing your own rendering/rasterizer code which operates on a 8 bit uint array representing the image pixels (R8G8B8). The operations you're proposing aren't too nasty, so if performance is unimportant, this might actually be the better way to go on the long run.