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Yes, you would have to had missed something, because having to have worked at the employer for 12 months prior to FMLA coverage is one of the base requirements.
You may have skipped the "Definition" section, because most people don't look there. Here is the regulation that defines what an "eligible employee" is.
In that regulation, under (2) (i) it indciates that an eligible employee is one that has been employed for at least 12 months by the employer