In a sense, she is right. The current recession isn't the fault of the state sector. However, the deficit quite clearly is.
Deficits occur because the government spends more money than it receives. (I know this should be obvious, but Toynbee appears to believe that taking money from people and spending it through an inefficient public sector somehow drives growth, so I can't assume anything). If we are run to deficit in the bad times (Keynsian economics), then the counter side to that is during the good times, you run a surplus, in order to be prudent and have some money in the bank to pay for the deficit in the bad times. The problem is that over the last 12 years, the government haven't felt the need to do that, spending it all on a splurge of increased public spending - believing the solution to any problem was a combination of top down targets and throwing more money at it - while simultaneously increasing the tax burden (the removal of the cap on NI, the increase in NI, the abolition of the 10p tax band) - all of which was presided over as Chancellor by the current Prime Minister (whose arrival in number 10 was greeted with such huge enthusiasm by Toynbee).
It may not be fair that the public sector might be carrying the can for a deficit that wasn't their fault - but nor is it fair that in the private sector there are hiring freezes and staff reduction programs in large companies for employees who aren't responsible for the recession either.