Evidence retrieval is a key component of explainable question answering (QA). We argue that, despite recent progress, transformer network-based approaches such as universal sentence encoder (USE-QA) do not always outperform traditional information retrieval (IR) methods such as BM25 for evidence retrieval for QA. We introduce a lexical probing task that validates this observation: we demonstrate that neural IR methods have the capacity to capture lexical differences between questions and answers, but miss obvious lexical overlap signal. Learning from this probing analysis, we introduce a hybrid approach for evidence retrieval that combines the advantages of both IR directions. Our approach uses a routing classifier that learns when to direct incoming questions to BM25 vs. USE-QA for evidence retrieval using very simple statistics, which can be efficiently extracted from the top candidate evidence sentences produced by a BM25 model. We demonstrate that this hybrid evidence retrieval generally performs better than either individual retrieval strategy on three QA datasets: OpenBookQA, ReQA SQuAD, and ReQA NQ. Furthermore, we show that the proposed routing strategy is considerably faster than neural methods, with a runtime that is up to 5 times faster than USE-QA.