Well, that's not entirely true, even if two random bits are independent, xor-ing them only gives you one random bit. What actually happens in Linux is that each new input of random bits gets pushed through a cryptographic hash, before being xor'd.
From replies it seems my two sentences weren't as clear as I thought. I'll try to refine it:
A property of bitwise xoring random variable `x` with a constant (or otherwise non-random but independent) value is that the entropy of `x` is preserved in the result.
However, xoring two arbitrary random variables is NOT guaranteed to preserve entropy. Preserving entropy only happens under certain specific conditions.
