The severity of the COVID-19 pandemic and the pace of its global spread have motivated researchers to opt for repurposing existing drugs against SARS-CoV-2 rather than discover or develop novel ones. For reasons of speed, throughput, and cost-effectiveness, virtual screening campaigns, relying heavily on in silico docking, have dominated published reports. A particular focus as a drug target has been the principal active site (i.e., RNA synthesis) of RNA-dependent RNA polymerase (RdRp), despite the existence of a second, and also indispensable, active site in the same enzyme. Here we report the results of our experimental interrogation of several small-molecule inhibitors, including natural products proposed to be effective by in silico studies. Notably, we find that two antibiotics in clinical use, fidaxomicin and rifabutin, inhibit RNA synthesis by SARS-CoV-2 RdRp in vitro and inhibit viral replication in cell culture. However, our mutagenesis studies contradict the binding sites predicted computationally. We discuss the implications of these and other findings for computational studies predicting the binding of ligands to large and flexible protein complexes and therefore for drug discovery or repurposing efforts utilizing such studies. Finally, we suggest several improvements on such efforts ongoing against SARS-CoV-2 and future pathogens as they arise.