Rather than being pushed by social services to meet any standards of care, the family, in particular the mother, was trusted to make decisions about how to deal with a problem they/she actually were inadequately prepared to address.
Why? Well richer people are often viewed as smarter and more capable. And as suggested in the article wealthier people are more defensive toward the psychiatric industry then poorer people.
So why would that be? IMO, one component of that is that wealthier people tend to have advanced educations and view themselves (rightly or wrongly) as smart and capable of assessing situations and making decisions. They also have access to information. In a manner much like sports fanatics, they read and accumulate lots of facts about mental disorders that impact their families. Not infrequently, parental awareness of media reports of trends and conflicts about treatments for the illness of their concern is as great or greater than a psychiatric professional's for that disorder. Granted such "mental disorder fans" lack the broader understanding of psychology and psychiatry, they may nonetheless see themselves as peers of health providers in child care decisions rather than subjects to professional expertise/authority. For such persons directives to intensive mental health care for a child may be viewed as merely suggestions...suggestions which can be dismissed.
Another component could stem from mental illness being attended with significant prejudice. Prejudice that often places a pall over family members of a mentally disordered person. Parents often perceive their goodness through attributes of their children, and so defend their children against demeaning dx's (e.g the vicarious attack on the parents' goodness). Just consider how successfully parental defense has pushed autism away from consideration as a mental disorder. Wealthier parents can deploy their education and money to engage lawyers to reinforce the parents' defensive bias. It isn't difficult to understand that the level of interest of mental health professionals and social workers is greater for providing care to those that will accept it than fighting those who reject it.