Some reinforcement learning (RL) algorithms have the capability of recombining together pieces of previously seen experience to solve a task never seen before during training. This oft-sought property is one of the few ways in which dynamic programming based RL algorithms are considered different from supervised learning (SL) based RL algorithms. Yet, recent RL methods based on off-the-shelf SL algorithms achieve excellent results without an explicit mechanism for stitching; it remains unclear whether those methods forgo this important stitching property. This paper studies this question in the setting of goal-reaching problems. We show that the desirable stitching property corresponds to a form of generalization: after training on a distribution of (state, goal) pairs, one would like to evaluate on (state, goal) pairs not seen together in the training data. Our analysis shows that this sort of generalization is different from i.i.d. generalization. This connection between stitching and generalization reveals why we should not expect existing RL methods based on SL to perform stitching, even in the limit of large datasets and models. We experimentally validate this result on carefully constructed datasets.This connection suggests a simple remedy, the same remedy for improving generalization in supervised learning: data augmentation. We propose a naive temporal data augmentation approach and demonstrate that adding it to RL methods based on SL enables them to successfully stitch together experience, so that they succeed in navigating between states and goals unseen together during training.