I don't know if its as simple as calling her a liar. People don't always include child benefit.
I'm well out of date with the benefits system, but it seems to me that if they have a reasonable enough wage to buy a 10 bedroom house they could easily not qualify for child benefit or tax credits. I don't know exactly how they work-do they take the number of kids into account when determining the cut off?
The kids do use school and so the taxpayer is paying for that, plus whatever NHS care the kids need.
But honestly, that's not something I can get especially worked up about. I don't use schools right now and I pay for them as a taxpayer. I want her kids to get a good education because its in my interests as a citizen that kids get a good education.
As said above, I have concerns about how well a family can provide an education for their kids in a family of this size and I do think its reasonable to enquire as to specific educational provision in that case. Quiverfull families, for example, would often be educating this size family with just the mother as teacher, possibly helped by the older girls (at the expense of their own further education). That's a problem, IMO. And one that would be resolved by, say, in the situation above, having two adults at home doing the education.
But the mere fact that they are producing a lot of educated future taxpayers...well meh, really. I'm more concerned that we're paying to educate a lot of kids quite badly than that there are some families who are doing what looks to be a good job of educating more kids than the average.