Seems to me that this is a direct corollary of the claim that people’s beliefs are affected at least somewhat by the data they are exposed to. This seems self-evidently true.

Maybe, but there's more to it.

(1) inconclusive means we may not have looked hard enough, or

(2) the effect may be very very small, as in not distinguishable from zero, or

(3) there are alternative models of learning. People could do bayesian updating, but they may also employ thresholds, toggle between belief systems and so on.

Summary: it's very complicated, lack of evidence suggests caution.

Maybe, but it's also possible that the people who LIKE crime shows tend to be less overly paranoid about it vs. people who just watch the news not necessarily expecting to see negative content, but do.