Summarizing documents with Large Language Models (LLMs) warrants a rigorous inspection of the resulting outputs by humans. However, unaided verification of generated outputs is time-intensive and intractable at scale. For high-stakes applications like healthcare where verification is necessary, expediting this step can unlock massive gains in productivity. In this paper, we focus on the task of evidence extraction for abstractive summarization: for each summary line, extract the corresponding evidence spans from a source document. Viewing this evidence extraction problem through the lens of extractive question answering, we train a set of fast and scalable hierarchical architectures: EarlyFusion, MidFusion, and LateFusion. Our experiments show that (i) our method outperforms the state-of-the-art by 1.4% relative F1-Score; (ii) our model architecture reduces latency by 4x over a RoBERTa-Large baseline; and (iii) pretraining on an extractive QA corpus confers positive transfer to evidence extraction, especially in low-resource regimes.