Actually I think it reads as if the headline misrepresents the thrust of the study - not that home learning has no effect at all, but that wealth and social status have much more effect. So even if I, as a graduate in a well-off household, don't consciously sit down and teach my child the alphabet, he'll still, at 5, have better outcomes in terms of academic and social skills than the child of more disadvantaged parents who may have been exposed to more formal learning.
This is from the TES article on the same report:
"Children with better educated mothers also displayed greater literacy and social skills. Children whose parents had degree-level qualifications were an average of six months ahead of their peers with less educated parents.
This remained true regardless of how often the wealthier or better-educated parents helped their children to learn, according to the research.
Parents with higher levels of education were better equipped to develop their children's academic interests, making connections between the curriculum and everyday experiences, Dr Hartas said.
"Educated parents are likely to interact with their children in different ways, and may be more resilient and resourceful when dealing with economic adversity."
Poorer parents cannot be expected to compensate with enthusiasm for their lack of education or financial resources, she added."