Excellent thoughts there, Matthew!

Several things to consider, even if the paper may have adjusted for wealth, it is not clear that they have also controlled for or adjusted for as you wrote isolation (geographical distance between the cultural arena and the place of living, availability of transportation) and most importantly as you mentioned "social network" and education. What they are reporting is perhaps a proxy of social network effect or perhaps even an educational effect, so people who tend to attend the cultural events are likely to have higher educational attainment than those who do not. Low educational attainment is also associated with depression, so the arrows go somewhat like as follows:

Cultural Outing <-- (enhances the chance of attending ) -- high level of Education -- (reduces the risk of) -- > Depression

similar to your argument that,

Cultural Outing <-- (reduces the chance of attending) -- Geographical and social Isolation -- (increases the risk of ) --> Depression

That being the case, if a negative association is found between cultural outing and depression even after adjustment of wealth, quite possible that there are these other variables that remain unadjusted.

Unfortunately in the Medium post, Jessica did not link to the main article she had drawn her conclusions, let's find that out and see. I am surprised that Harris Sockel decided to amplify Jessica's conclusion without first fact checking.