There is a terrific assumption from Cameron and much of this discussion (especially Attachment theory), and that parents are always responsible for shaping a child's character and thus should be blamed when things go wrong. This is by no means a fact.
Indeed if a child is brought up in a crime-ridden area, they will be susceptible to committing these same kinds of crimes. This is because of the high rate of peer pressure and the want to fit in to the group, not necessarily parenting. Even if the parents try to bring up their children the best way possible, chances are that if they associate with delinquents, they will become one. You can be pretty sure of this because if you take a child who is succumbing to crime and move him to new environment with less crime as the norm, chances are he will get himself on the right track, because he is trying to fit in with a new peer group.
So parents should not be always to blame. Up until a couple hundred years ago, people lived in groups that extended far beyond the nuclear family. So children were influenced by a number of people, not just their parents. People also need to realize that a lot of personality traits come from their genes, not their parents nurturing, as this can be seen in the separated twin studies.
Children will not use everything that they learned from their parents. Children learn how to behave, for the most part, from other people in their social group. Adults do the same; they act more like the people in their social groups rather than their parents.
This nurture assumption leads parents to believe that if they mess up somehow in raising their child, they will mess up their child's life. Parents are sometimes held responsible if their child commits an illegal act but parents may have no control over their child when it comes to something like this. They can raise their child in the most loving home, yet he can still become a criminal loser.
What I think Cameron is reciting is research from Lareau which shows that there are more successful children should their parents have a style called "concerned cultivation" in which parents "foster and assess a child's talents, opinions and skills", whereas on the other side of the fence (and they often quoted as the working class values), there is a parenting strategy of "accomplishment of natural growth", which basically means just leave 'em to it. The research shows that although there is a fine line between being pushy and preparing, the concerned cultivation parents definitely give children bureaucratic advantages and a sense of entitlement ( in the best possible sense of the word). In fact, these children grow up advocating for themselves, asking questions and comfortably interacting with adults.
As ever, parenting is just one small factor associated with the outcome of children, but if the research quoted above is reliable then I hate to say it, but I can only see this as being a responsible opinion. I don't see it as an argument in refusing benefits at all........it is not a monetary argument, more an ideological one.