Right, but that's just one part of why I'm a (nonsuperdeterministic) local determinist who thinks the mainstream LR program was effectively ruled out by Bell almost 50 years ago.
Or rather, because entangled photons measured at polarizers oriented at the same angle behave identically, and also because rate of joint detection varies as θ varies, then it's assumed that the underlying parameter that's determining joint detection isn't varying from pair to pair. And because individual detection doesn't vary as the polarizer setting varies, then it's assumed that the underlying parameter that's determining individual detection is varying from pair to pair. Hence, the assumption that there is a different underlying parameter or function determining coincidental detection and individual detection. But the LR program requires that coincidental detection be modelled in terms of the same underlying parameter or function that's determining individual detection.