The initial observation is that one can preserve privacy w.r.t queries that are Lipschitz functions, but hell may break loose otherwise. The idea, then, is to ``filter'' the queries through a reconstruction interface that preserves the functionality of legitimate queries (corresponding to Lipschitz functions) and modifies illegitimate queries to legitimate ones. The point to stress is that this interface operates without assuming anything on the syntax of legitiamte queries; it rather operates on their semantics (or functionality). This is done by running a (local) reconstruction algorithm that maps functions to functions (such that Lipschitz functions are mapped to themselves).
See ECCC TR11-057.