But you have nothing to compare that rate to. The assertion was a connection between financially supporting people in certain situations and the rate at which those situations occur, and your counterexample doesn't address that. A plausible mechanism seems pretty obvious - you're making divorce easier, so a few borderline cases shift over the edge.
"Wet houses"-- subsidized housing for alcoholics (they need to get most of their own money for alcohol, but their other expenses are covered) might actually be a good idea. It's cheaper than trying to get them to stop drinking, arguably kinder than trying to get people to take on a very hard task that they aren't interested in, and leads to less collateral damage than having alcoholics couch-surfing or living on the street.
Utilitarians, what do you think?