Why can a device that makes random bits by measuring photon pairs sent to two distant detectors support the claim that its bits are truly random when the two measurements are correlated, rather than weaken it?

Answer: The matches are too strong for any shared pre-set plan, so the outcomes cannot be prewritten.

The photons become identical copies, so any hidden difference that could predict them is erased. — It is true that the two photons are linked by the experiment, and each single outcome can look random. But they do not need to become identical copies; they can remain distinct particles with linked measurement results. If they were just identical copies, their outputs would tend to duplicate rather than supply fresh independent randomness.

The correlation cancels detector noise, so only the genuinely random signal remains. — Detector noise is a real practical issue and can remain even when results are correlated. Correlation does not subtract that noise or make the machine perfect. The randomness claim comes from a match pattern that no shared pre-set plan could reproduce, not from cleaning up the signal.

The matches are too strong for any shared pre-set plan, so the outcomes cannot be prewritten. ✓ — The individual measurements can look unpredictable while the paired results line up in a special pattern. That pattern can be stronger than any shared pre-set instructions could make it. If no shared instructions can explain the matches, the outcomes cannot have been fixed in advance, so they can confirm fresh random bits.