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Traditionally, recommendation algorithms have been designed for service developers. However, recently, a new paradigm called user-side recommender systems has been proposed and they enable web service users to construct their own recommender systems without access to trade-secret data. This approach opens the door to user-defined fair systems even if the official recommender system of the service is not fair. While existing methods for user-side recommender systems have addressed the challenging problem of building recommender systems without using log data, they rely on heuristic approaches, and it is still unclear whether constructing user-side recommender systems is a well-defined problem from theoretical point of view. In this paper, we provide theoretical justification of user-side recommender systems. Specifically, we see that hidden item features can be recovered from the information available to the user, making the construction of user-side recommender system well-defined. However, this theoretically grounded approach is not efficient. To realize practical yet theoretically sound recommender systems, we propose three desirable properties of user-side recommender systems and propose an effective and efficient user-side recommender system, \textsc{Consul}, based on these foundations. We prove that \textsc{Consul} satisfies all three properties, whereas existing user-side recommender systems lack at least one of them. In the experiments, we empirically validate the theory of feature recovery via numerical experiments. We also show that our proposed method achieves an excellent trade-off between effectiveness and efficiency and demonstrate via case studies that the proposed method can retrieve information that the provider's official recommender system cannot.