I fail to see how our primate ancestors ability to socialize outside of church somehow disproves that removing a large social component in modern American life could lead to less social support.
I just did a quick google search on church affiliation and suicide rates (to bring this back to the original article and my hypothesis), here's an interesting study published in the American Journal of Psychiatry on the topic:
So at least one study seems to support the hypothesis (interesting that it also showed increased substance abuse, which was also discussed as one of the culprit's of the higher death rate for white men).