The rapid advancement of Large Language Models (LLMs) has transformed conversational systems into practical tools used by millions. However, the nature and necessity of information retrieval in real-world conversations remain largely unexplored, as research has focused predominantly on traditional, explicit information access conversations. The central question is: What do real-world information access conversations look like? To this end, we first conduct an observational study on the WildChat dataset, large-scale user-ChatGPT conversations, finding that users' access to information occurs implicitly as check-worthy factual assertions made by the system, even when the conversation's primary intent is non-informational, such as creative writing. To enable the systematic study of this phenomenon, we release the WildClaims dataset, a novel resource consisting of 121,905 extracted factual claims from 7,587 utterances in 3,000 WildChat conversations, each annotated for check-worthiness. Our preliminary analysis of this resource reveals that conservatively 18% to 51% of conversations contain check-worthy assertions, depending on the methods employed, and less conservatively, as many as 76% may contain such assertions. This high prevalence underscores the importance of moving beyond the traditional understanding of explicit information access, to address the implicit information access that arises in real-world user-system conversations.