I think there may be some truth in this. I'm an educated mum who had children later in life so took time off work, and could afford clubs and swimming etc. A group of us went to some baby classes at the local Surestart centre but we could have gone elsewhere.
When DS was 2 I suspected possible issues so took him to a parenting class at the centre. They were great - suggested he start pre-school (which I was fortunate enough to be able to afford) so I did, and the staff there were fantastic helping me get his ASD diagnosis.
Meanwhile I attended a local authority parenting course - every wednesday afternoon for ten weeks or whatever. It wasn't overly helpful as our issues related to what turned out to be SEN rather than 'normal' parenting problems - but we didn't know that at the time. But I noticed that all the parents who turned up regularly were people like me - well educated, with no personal issues, just wanting to do the best for their children. We could probably have learned the same from reading a few books. But for the first two weeks a young couple came with their daughter, and they were clearly desperately in need of support. They were also very uncomfortable about being in a 'class', speaking in front of others, etc. Their child wouldn't go to bed apparently - she was about three and wandered about doing her own thing, with a snotty nose, and they were clearly out of their depth. The chap kept on and on about going to the pub.
I think they had been referred by some body or other - but they stopped coming after a couple of classes as I think they just felt too uncomfortable. It's such a shame - but the council put on these amazing resources and it's the wrong people who go! You can't make people attend, even if they would really benefit - and also perhaps having some there who don't need it so much may make those struggling parents feel even more out of their comfort zone.
I don't know the answer - how to reach those most in need - but maybe these centres and courses aren't the best way?
I work in a school and it's the same for things like parents evening. The articulate, engaged, supportive parents all come along and the ones that the teachers really want engage with are often the ones who don't.