I think the economic status of one's family would affect her later life. Just as the textbook stated, the proportion of children showing "secure" attachment is lower in lower income families. It shows that how much care one receives is correlated with the amount of attention a child receives.
Though a family's economic status may have some affect on a child's wellbeing later in life, I believe this factor makes significantly less impact then their attachment to parents. With low income families the parents may work away from home more often, which may lead to insecure attachment, but there are studies showing that, at a fairly low salary, happiness and income stop correlating.
I agree that that income correlates with wellbeing in an overwelming number of cases. Poor being end up poor. For simplicities sake I'm using wealth as a measure of wellbeing. However, it's likely that income also correlates with how much time mothers have to spend with their babies and therefore it's hard to tell if income is the direct cause of the wellbeing.