It's funny that world-leading physicists were arguing about these questions in the 40s (even if briefly), because I feel like nowadays, everyone who has played Civilization would've intuitively known Whittaker's argument to be flawed (at least those of us that like to savescum). A photon with hidden variables is essentially like playing a game of Civilization with the "preserve random seed" option enabled: if you reload a save and then take the same action (e.g. order unit X to attack unit Y) 100 times, you'll get 100 times the same result (e.g. unit X wins) — just like a deterministic photon would always take the same path. But if you load that same save and then take a different action (e.g. first order unit A to attack unit B, and then order unit X to attack unit Y) you may get a different outcome (e.g. unit X might die), because the PRNG from that same random seed is fed operations in a different order. The result can still be absolutely deterministic, but nevertheless dependent on external inputs. Same for the photon that could start acting differently in a way that is still tied to its hidden variable state when the environment it is confronted with changes (as if each quantum particle was seeded with its own little PRNG).

Of course Bell later proved by experiment that quantum state cannot be explained as simply as a local hidden variable, no matter how it looks like. But these guys didn't know that yet.