In this particular case there's also the simpler, more technical/mathematical argument: you cannot possibly just "accidentally" have that exact noise. Getting those specific bits instead of any other sequence from the space of random numbers that much long requires you to extend effort at least equivalent to possession of the exact copyrighted work that happens to fall out of the XOR exercise.
Except there are two people, B and C with noise. The only thing you can prove is that if you XOR both noise vectors together, you have a copyrighted work.
Both people will say they are innocent and that the other person used the other's noise vector and the copyrighted work to produce their noise vector.