Personalization services, such as recommender systems, operate on vast amounts of user-item interactions to provide personalized content. To do so, they identify patterns in the available interactions and group users based on pre-existing offline or online social relations, or algorithmically determined similarities and differences. We refer to the relations created between users based on algorithmically determined constructs as algorithmically mediated user relations. However, prior works in the fields of law, technology policy, and philosophy, have identified the lack of existing algorithmic governance frameworks to account for this relational aspect of data analysis. Algorithmically mediated user relations have also not been adequately acknowledged in technical approaches, such as for data importance and privacy, where users are usually considered independent from one another. In this paper, we highlight this conceptual discrepancy in the context of recommendation algorithms and provide empirical evidence of the limitations of the user independence assumption. We discuss related implications and future practical directions for accounting for algorithmically mediated user relations.