Egocentric video action recognition under domain shifts remains challenging due to large intra-class spatio-temporal variability, long-tailed feature distributions, and strong correlations between actions and environments. Existing benchmarks for egocentric domain generalization often conflate covariate shifts with concept shifts, making it difficult to reliably evaluate a model's ability to generalize across input distributions. To address this limitation, we introduce Ego4OOD, a domain generalization benchmark derived from Ego4D that emphasizes measurable covariate diversity while reducing concept shift through semantically coherent, moment-level action categories. Ego4OOD spans eight geographically distinct domains and is accompanied by a clustering-based covariate shift metric that provides a quantitative proxy for domain difficulty. We further leverage a one-vs-all binary training objective that decomposes multi-class action recognition into independent binary classification tasks. This formulation is particularly well-suited for covariate shift by reducing interference between visually similar classes under feature distribution shift. Using this formulation, we show that a lightweight two-layer fully connected network achieves performance competitive with state-of-the-art egocentric domain generalization methods on both Argo1M and Ego4OOD, despite using fewer parameters and no additional modalities. Our empirical analysis demonstrates a clear relationship between measured covariate shift and recognition performance, highlighting the importance of controlled benchmarks and quantitative domain characterization for studying out-of-distribution generalization in egocentric video.