Embeddings produced by pre-trained deep neural networks (DNNs) are widely used; however, their efficacy for downstream tasks can vary widely. We study the factors influencing out-of-distribution (OOD) generalization of pre-trained DNN embeddings through the lens of the tunnel effect hypothesis, which suggests deeper DNN layers compress representations and hinder OOD performance. Contrary to earlier work, we find the tunnel effect is not universal. Based on 10,584 linear probes, we study the conditions that mitigate the tunnel effect by varying DNN architecture, training dataset, image resolution, and augmentations. We quantify each variable's impact using a novel SHAP analysis. Our results emphasize the danger of generalizing findings from toy datasets to broader contexts.