Are Mexicans sicker because of socialized medicine?

Writing in Best of the Web Today of the Online Wall Street Journal, James Taranto points out  a devastating fact about Mexico, hit hard by the outbreak of swine flu.  Mexico, which has had about 70 swine flu deaths out of  1000 cases, a fatality rate of 7%  which

is far higher than the 2.5% fatality rate from the Spanish flu pandemic of 1918-19, although the latter was many orders of magnitude more widespread, killing 40 million people world-wide.
Why such a high rate in Mexico?  Taranto speculates because the government provides health care"? Or, as he mocks

But . . . but . . . Mexico has socialized medicine!
What?!  Is it possible that citizens that have access to "free" medical care, available to all, are actually sicker than those who don't?  Apparently so.