If I'm being particularly generous I can see that maybe for a short period it would be more challenging than you'd expect it to be on that salary.
x2 children in nursery or private school 2000-3000
rent on a 3 bed house 1600
Travel £200 p/month each, £400
Bills and council tax £500
That still leaves £1500 for living expenses although it's possible I missed something out, although with four children I imagine that could go pretty quickly.
Still a ridiculous point she's making, they should manage their finances a bit better/move to a cheaper area/rent somewhere with good state schools to save on school fees.