We revisit the reference determinacy (RD) assumption in the task of natural language inference (NLI), i.e., the premise and hypothesis are assumed to refer to the same context when human raters annotate a label. While RD is a practical assumption for constructing a new NLI dataset, we observe that current NLI models, which are typically trained solely on hypothesis-premise pairs created with the RD assumption, fail in downstream applications such as fact verification, where the input premise and hypothesis may refer to different contexts. To highlight the impact of this phenomenon in real-world use cases, we introduce RefNLI, a diagnostic benchmark for identifying reference ambiguity in NLI examples. In RefNLI, the premise is retrieved from a knowledge source (i.e., Wikipedia) and does not necessarily refer to the same context as the hypothesis. With RefNLI, we demonstrate that finetuned NLI models and few-shot prompted LLMs both fail to recognize context mismatch, leading to over 80% false contradiction and over 50% entailment predictions. We discover that the existence of reference ambiguity in NLI examples can in part explain the inherent human disagreements in NLI and provide insight into how the RD assumption impacts the NLI dataset creation process.