Will government involvement drive up health-care costs?

Opponents of a public health-insurance plan pose two main objections: that it will create an 'unlevel playing field' that will harm the private market for insurance (an odd objection, since that playing field already tilts quite sharply away from patients' pockets and health and toward the wallets of the health-insurance industry); and that government involvement will raise costs.
These objections seem to hold sway to the degree we limit our discussion to what already exists in the U.S. As with squabbles about the problems with our educational (non)system, the picture gets clearer if we step back and test this argument against the larger world.
In an article in Forbes, Bruce Bartlett brings some clarity by doing just that:

We spend $7,290 per person on average versus $2,964 among all OECD countries. Norway, the nation with the second most expensive health system on a per capita basis, spends $4,763. (Currency conversions based on purchasing power parity.)
Of course, Americans know that they pay a lot for health; the rising cost of health insurance for employers is the main reason why wages have been stagnant for years. [NB from DD: Actually, many Americans manage to ignore this, because they don't feel the connection; they know their wages aren't going up, but because they never see the money that the employers pay for premiums, they don't really feel the loss. Put it in their hands and take it out again -- the experience I have as a freelancer -- and you damn well feel it.] But they also fear that any further expansion of government involvement in the health care system will only make it more expensive. This is a key objection to the health care reform bill now working its way through Congress.
The international data, however, show no evidence that increasing government's share of health care expenditures raises health spending as a share of GDP. The top five countries with the highest government share of total health outlays spend almost exactly the same percentage of GDP on health as the lowest five countries excluding the U.S.: 8.2% of GDP on average for the former versus 8.3% of GDP for the latter. (I left out the U.S. because it skews the data; the bottom five countries including the U.S. spend 9.7% of GDP on health on average.)