The topic of discussion is suicides. Read the sentence in the proper context.
Your causal interpretation is not exclusive.
In general people who believe in God are much happier than athiest and their belief in God gives them strenght through tough times, which is why they can live peacefully in third world countries while atheist are killing themselves despite living in much better conditions.
Populations living in the countries you've named, are not living "peacefully" - so, perhaps, their lower suicide rates are due to something other than their purported 'happiness' as believers in a god.
Maybe their belief in a god feeds apathy: they may believe themselves powerless to change their current condition, and so do nothing except... stew, and wait for a god to help them.
Maybe their belief in a god stirs them to fear of releasing themselves from the inescapable (see the point above) misery and inadequacy of their lives. They dare not find release/relief in suicide, less their god condemn their lingering consciousness to an even worse fate... eternally.
Conjectures of causal relationships aside, I would definitely say that poverty is worse for one's health, than is atheism.