We study the foundations of empirical equilibrium, a refinement of Nash equilibrium that is based on a non-parametric characterization of empirical distributions of behavior in games (Velez and Brown,2020b arXiv:1907.12408). The refinement can be alternatively defined as those Nash equilibria that do not refute the regular QRE theory of Goeree, Holt, and Palfrey (2005). By contrast, some empirical equilibria may refute monotone additive randomly disturbed payoff models. As a by product, we show that empirical equilibrium does not coincide with refinements based on approximation by monotone additive randomly disturbed payoff models, and further our understanding of the empirical content of these models.