Diagnostic reasoning is a key component of expert work in many domains. It is a hard, time-consuming activity that requires expertise, and AI research has investigated the ways automated systems can support this process. Yet, due to the complexity of natural language, the applications of AI for diagnostic reasoning to language-related tasks are lacking. To close this gap, we investigate diagnostic abductive reasoning (DAR) in the context of language-grounded tasks (NL-DAR). We propose a novel modeling framework for NL-DAR based on Pearl's structural causal models and instantiate it in a comprehensive study of scientific paper assessment in the biomedical domain. We use the resulting dataset to investigate the human decision-making process in NL-DAR and determine the potential of LLMs to support structured decision-making over text. Our framework, open resources and tools lay the groundwork for the empirical study of collaborative diagnostic reasoning in the age of LLMs, in the scholarly domain and beyond.