Whether large language models (LLMs) process language similarly to humans has been the subject of much theoretical and practical debate. We examine this question through the lens of the production-interpretation distinction found in human sentence processing and evaluate the extent to which instruction-tuned LLMs replicate this distinction. Using an empirically documented asymmetry between pronoun production and interpretation in humans for implicit causality verbs as a testbed, we find that some LLMs do quantitatively and qualitatively reflect human-like asymmetries between production and interpretation. We demonstrate that whether this behavior holds depends upon both model size-with larger models more likely to reflect human-like patterns and the choice of meta-linguistic prompts used to elicit the behavior. Our codes and results are available here.