You don't think it's possible that an LLM's internal machinery could decide that an underused-by-humans word should be used more frequently in output than it sees in input because it maps cleanly onto a frequently needed semantic? I think that's possible
It sounds like you are trying to understand LLM behavior using a mental model that inaccurately personifies the stochastic parrot.
A more parsimonious explanation is that this term got more-or-less randomly boosted by the reinforcement learning loop because there was nothing in the training data to discourage its use.