The non-cohabiting group may have more money, may be more secure in their jobs, or may be older. Being at a secure point in their life may mean that marriage is more attractive, AND financial security may mean there are fewer stresses during the marriage, thus decreasing chance of divorce. They try to match two groups on as many of the other potential variables as possible. This would include issues that the callers brought up, such as finances and religious beliefs. But even this won't work, as a thought experiment will make clear.
Scientists often work from experiments of nature.
We can imagine an experiment of nature which accidentally ends up effecting random assignment. Imagine a group of couples desiring marriage. After they've decided to marry, a political or natural disaster happens and communities are thrown into relocation camps or disaster shelters. The disaster happens at a time such that some couples have just been married, but other couples' weddings were still pending. They were going to be married and then were kept from it artificially.