Generative text-to-image models enable us to synthesize unlimited amounts of images in a controllable manner, spurring many recent efforts to train vision models with synthetic data. However, every synthetic image ultimately originates from the upstream data used to train the generator. Does the intermediate generator provide additional information over directly training on relevant parts of the upstream data? Grounding this question in the setting of image classification, we compare finetuning on task-relevant, targeted synthetic data generated by Stable Diffusion---a generative model trained on the LAION-2B dataset---against finetuning on targeted real images retrieved directly from LAION-2B. We show that while synthetic data can benefit some downstream tasks, it is universally matched or outperformed by real data from the simple retrieval baseline. Our analysis suggests that this underperformance is partially due to generator artifacts and inaccurate task-relevant visual details in the synthetic images. Overall, we argue that targeted retrieval is a critical baseline to consider when training with synthetic data---a baseline that current methods do not yet surpass. We release code, data, and models at https://github.com/scottgeng00/unmet-promise/.