Recent work shows that causal facts can be effectively extracted from LLMs through prompting, facilitating the creation of causal graphs for causal inference tasks. However, it is unclear if this success is limited to explicitly-mentioned causal facts in the pretraining data which the model can memorize. Thus, this work investigates: Can LLMs infer causal relations from other relational data in text? To disentangle the role of memorized causal facts vs inferred causal relations, we finetune LLMs on synthetic data containing temporal, spatial and counterfactual relations, and measure whether the LLM can then infer causal relations. We find that: (a) LLMs are susceptible to inferring causal relations from the order of two entity mentions in text (e.g. X mentioned before Y implies X causes Y); (b) if the order is randomized, LLMs still suffer from the post hoc fallacy, i.e. X occurs before Y (temporal relation) implies X causes Y. We also find that while LLMs can correctly deduce the absence of causal relations from temporal and spatial relations, they have difficulty inferring causal relations from counterfactuals, questioning their understanding of causality.