If the majority of your funding comes from the government, you're not a charity, you're an agency (quango, arms-length authority, whatever). Rather like the NSPCC, no matter how good the work KC does, by straddling the third and the public sector they avoid a lot of the constraints of the former and lot of the governance of the latter, and can spend central government money a lot more freely than the government itself can. They're not subject to Freedom of Information, even though they are in large part doing the work of the state funded by the state. Their ever-present cry that social services aren't doing enough would be easily answered by taking the money they're getting and giving it to social services.
Batmanghelidjh is a high-profile example of a common issue with charities: that what starts out as the laudable work of an individual funded by cake sales and small donations rapidly becomes a larger, more complex organisation. The skills to start a charity, and campaign on the charity's issues, are not the skills required to run a large organisation, but the founder is usually reluctant to let go. Government funding the follows and with it a certain amount of oversight, but by that stage the organisation has become something of a cult of personality; it's the difference between genuinely large organisations with appropriate governance and audit and small organisations that got large whilst remaining, at heart, small.
Someone up thread has referenced the (contested, and rather thing) Speccie article, and it in turn links to various things by disgruntled former employees. The comments make interesting reading, too. You need to bear in mind that disgruntled former employees often have it in for perfectly decent organisations, but on the other hand it was disgruntled former employees that were shouting for years about the News of the World and about Lance Armstrong: just because someone has a motive to lie doesn't make them a liar.
My gut feel is that CB is a decent woman with a rather large ego who has surrounded herself with something of a claque and has played government hard to the point that they're now asking awkward questions about governance, and the KC is a decent charity that does good work but probably also has some stuff going on that could be better run. They're getting a lot of government money, their governance is obstructing running it properly, and CB should get on with what she does well - appearing on TV and campaigning for people who have no voice - and do rather less of being a chief executive, for which she is unqualified and doesn't appear very good at (real CEOs don't appear on Today at 10 to 8 making wild accusations about government conspiracies to silence them coming all the way from Number 10, for example, because it makes them sound unhinged).