Well, the most relevant counterexample here would be the California Health and Safety Code Sec. 50052.5 [0], which provides the cost-based definitions of "affordable housing" which apply to various income tiers (which are also those relevant to the present proposal from Gov. Brown.)

(These definitions are often prerequisites to certain subsidies, but it is meeting the definition, not the subsidy, that makes it "affordable housing".)

> The "affordable" units are turned over to a government agency

Proposals (including the present one from Gov. Brown [1]) conditioned on a certain share of affordable housing usually require that the developer make a commitment that they will meet the applicable cost-based definition of "affordable" for a period of time, and that that commitment will be enforceable by a public agency (the present proposal requires that this be done by the developer recording a land-use restriction enforceable by the public agency.)

This does not require that the property be turned over to (or even managed by) a public agency, though certainly there are affordable housing developments that have occurred where there was either direct ownership or management of the units by a public agency, nor does it require that the housing be subsidized in any way (though at the "lower income" tier, the population for whom they are targeted to be "affordable" to is also the population eligible for Section 8 housing subsidies, I believe.)

[0] http://www.leginfo.ca.gov/cgi-bin/displaycode?section=hsc&gr...

[1] http://www.dof.ca.gov/budgeting/trailer_bill_language/local_...