I think this all revolves around what the person means by "free market" Some people think this is a "free-for-all" while in fact a free market is usually regulated to some fashion to make it free (by guaranteeing private property rights and tort law for contract enforcement, if nothing else) So free market definitely does not mean lack of government support/definition/intervention.
Taking, for instance, the health insurance industry in the U.S.. I'm in favor of the government defining simple levels of insurance coverage, say from A to F. A would be total coverage for anything that went wrong (including preventive care). F might be catastrophic care only, with the guarantee that life-saving measures do not bankrupt the family (even is some measures might be denied).
In this case, the government can and should intervene to create the open market. Currently policies are so obfuscated by legalese that consumers effectively have no choice. In details-rich markets, like lending, insurance, airline fares, etc, the government can make the market freer by simply providing _simple_ standard categories of service.
As far as direct intervention in social systems, such as education, I think most right-leaning libertarians such as myself would support those interventions that directly related to things the government absolutely had to do. Education falls into that category because the need of a national army requires a standard of education. Health care in general is a very tricky area. We're developing life-saving cures for our elderly that cost more than the person made during their working years. I find it very hard to believe people in a democracy are going to vote for their own early deaths, so as a practical matter some kind of political appeasement needs to be made with the public at large, free market or not. I'm still thinking this one through.
The danger is taking a complex system and oversimplifying whether on the "leave it alone and everything will be fine" side or the "hey, we can engineer this thing to do whatever we want" side. It's way too complex to work like political slogans want us to believe. I think we're in agreement on this point.
If I'm not mistaken, this is similar to the Warren Buffet view of the economy: yeah, get the government out of the market where it makes sense, let the market do its work, but then whoever wins needs to share some of that with the poorest in our society.