It is true. Self insurance is a sensible thing to do if you are large enough to be able to swallow a few big losses, as any insurance company will calcualte the same risks plus add in some profit.
The disadvantages of this are:
1 - the insurnace market operates in a 5 to 10 year cycle. When insurance is cheap it is called the "soft" market and this occurs when insurnace companies are keen to get business. When it is expensive this is called the "hard" market and this occurs when the new entries to the market have some big losses and decided they don't want ot play any more. In some soft times insurance can cost less than it should even those who self insure might be better off buying underpriced cover in the open market.
2 - insurnace companies employ people like me who go round and tell you to install fire detection or move the bins away, this reduces their losses. If those who self insure don't manage their risks well, they might have more losses than they can afford.
All local authorities used to self insure in a big pot. It was called Municipal Mutual. It went bust becase no matter hw much they put the premiums up by the losses kept growing. Partly due to bad risk management, partly cos they paid out on every claim, even those that were not covered by the policy.
Zurich Municipal took over Municipal Mutual about 13 years ago I think and kept many of the staff, which is why they tend to understand local authorities pretty well and still are the main player in a market that many insurers are still scared off due to the school fire problem.
So in summary, good risk management is the key to insurance.
In recent times some local authorities, Hampshire I think self insure. As does the NHS. It is also common for massive UK companies. Self insurers (captives) tend to be run from tax haven such as Bermuda.