Final answer:
The incorrect statement about internal service funds is that costs are reported twice within the same set of financial statements, which is not true as these costs are recorded only once to prevent double counting.
Step-by-step explanation:
The statement that is not true about internal service funds as reported in the fund financial statements is that 'costs reported by internal service funds are reported twice within the same set of financial statements.' This is not correct because the costs are recorded only once. Instead, when internal service funds provide goods or services to other departments within the same government, these transactions are recorded as revenues for the internal service fund and expenses for the receiving department, preventing any double counting of costs.
Billing rates for internal service funds should indeed be set to cover the full costs of providing the goods or services, which includes factors such as depreciation. Furthermore, it is correct that the established billing rates can include the allocation of depreciation, which means that governmental funds using the services will indirectly recognize depreciation as part of their operating expense. Lastly, while adjustments to billing rates for internal service funds can be used to manage surpluses or deficits, this should not be done to transfer deficits or surpluses to the general fund in a way that is not reflective of the true cost of services provided.