I'm not disagreeing with you, but I have not frequently heard the phrase "fair market" (as opposed to a far more limited and specific term "fair market value", where "fair" I believe applies to "value" and not "market") and would be interested in hearing more of its definition and criteria.

Trivially, I would assume proponents of "free market" and "fair market" are a tiny if not zero Venn diagram, and that terms are at least somewhat opposing, but will withhold my judgement :-).