You disagree, then, with Pearl's dictum that causality is a primitive concept, not reducible to any statistical construction?

No. For example, AIXI is what I would regard as essentially a Bayesian agent, but it has a notion of causality because it has a notion of the environment taking its actions as an input. What I mean is more like wondering if AIXI would invent causal networks.

It is generally understood as the former; attempts to fix it consist of changing it to use the latter.

I think this is too narrow a way to describe the mistake that naive EDT is making. First, I hope you agree that even naive EDT wouldn't use statistical correlations in a population of agents completely unrelated to it (for example, agents who make their decisions randomly). But naive EDT may be in the position of existing in a world where it is the only naive EDT agent, although there may be many agents which are similar but not completely identical to it. How should it update in this situation? It might try to pick a population of agents sufficiently similar to itself, but then it's unclear how the fact that they're similar but not identical should be taken into account.

AIXI, by contrast, would do something more sophisticated. Namely, its observations about the environment, including other agents similar to itself, would all update its model of the environment.

I don't follow the reference class part, but it doesn't seem to cover the situation of an EDT reasoner advising someone else who professes an inclination to smoke.

It seems like some variant of the tickle defense covers this. Once the other agent professes their inclination to smoke, that screens off any further information obtained by the other agent smoking or not smoking.

It is also a problem that AIXI can be set to solving. What might its answer be?

I guess AIXI could do something like start with a prior over possible models of how various actions, including smoking, could affect the other agent, update, then use the posterior distribution over models to predict the effect of interventions like smoking. But this requires a lot more data than is usually given in the smoking lesion problem.