My disproof is done
The joint probability result is the one that is supposed to be impossible without spooky superluminal action at a distance, but here it operates in an ordinary manner (if ‘moving tangent vectors’ can be considered ordinary objects). To make the counterproof even more devastating, the ‘correlations’ are between two experimental runs on the same apparatus.
To reproduce the error made by the orthodoxy, instead of doing an integration over theta, you would do a double integration over two different variables, one for each cosine-square in the integrand. This error is what is ‘justified’ by claiming it ‘encodes’ ‘locality’.
It’s absolutely astonishing what theoretical physics has become, but then it seems less so when I consider how overblown the reputation of physicists is in our society. We would actually expect such incompetence and orthodoxy in many other academic fields.