If it occurred at exactly the same rate, I'd still expect it to have a downward effect on family income. I mean, it would be extremely surprising if the additional burden of needing to care for a family member with any kind of illness increased income.
That's fair, and I should check myself. I got so caught up in everyone's solecistic discussion of causality that I missed the line in the paper where they specifically disclaim that this is a causal association.