Replace the system with one that chooses A only; replace it with one that chooses B only; analyze distributions; analyze original system.

Or replace A with known non-random source, and then B, and analyze.

I'm not sure what the argument is though. If something has an effect, there will be a correlation. Measuring the correlation may require modifying the system. We've known that measurement unavoidably affects the system under measurement for some time now. It's just a matter of degree.