I love the way you assume that those women have been brainwashed by the Sun and the Mail, op. 
I live on a mixed estate of Owner Occupier and Housing Association, and we have a few families that have been living off benefits since the mid 90s. To say this annoys some of the other families on the estate would be an understatement. Interestingly, the people that get really apoplectic about it are those that also live in the HA houses but go out to work and pay rent -- probably because they have exactly the same lifestyle as the benefit families (same homes, same landlord, same costs), only they have to get up at 6.30am every day and work Saturdays to boot.
Maybe it is down to where I live and grew up, but I really do think some people live on another planet when it comes to this issue. To me, the idea that benefits are not seen by many people as an alternative way to fund their life choices is just bizarre.
I can only imagine those people live in very nice areas and went to nice schools. 
I know a lot of people that live off benefits: friends, family members, old school friends, children of my parent's friends, neighbours. An old ex-boyfriend of mine even managed to claim the full range of disability benefits during the noughties, and saved huge amounts of money by living in India for nine months of every year. Those benefits just piled up and up in his bank account. Over the last twenty years, he has probably worked for about eighteen months in total, but still has a rather nice one bed flat in a conservation area of London, seventeen years worth of rent paid for by housing benefit of course, and a fat wedge in the bank, courtesy of the tax-payers of Britain.
I can't actually think of one case where the person or family in question actually has an issue with disability or illness, or was pushed into claiming because of family breakup.