Fundamentally, it IS true though. You only have to look at Reception intake in different socio-economic areas to see how true it is.
We live in a very middle class village, the vast majority of parents are in professional occupations, a significant proportion of mums are SAHM by choice, house prices are very high but so are many families' incomes. So, by definition it is a 'rich' area.
The children arrive into reception knowing how to sit and listen, they know how to eat using a knife and fork, many know some letters, many can write their names, most can count and dress and undress themselves, they are toilet trained and, for the most part, have reasonable social skills for 4yos.
Compare that to the school where DH used to work.
It's on an inner city estate, the vast majority of parents are 2nd and 3rd generation unemployed, they live in council houses, they claim benefits. There is a significant drug problem on the estate, a significant percentage of the children are known to SS; several are in care. It is a very, very deprived area.
The reception teacher in that school spends that year teaching the children how to dress themselves, how to sit quietly, how to listen. She has to actively work at improving their concentration. They have to be taught how to use a knife and fork, how to play with their peers. These are children who have spent most of their early lives sat in front of a TV screen. Not all of them, of course, but the majority.
If she's lucky, by the easter term she may be able to start teaching phonics and number work.
Unfortunately, for too many children growing up in these sorts of 'poor' areas, that research is very, very accurate and, tbh, you must be quite naive if you think that socio-economic background has no bearing at all on a child's development.