It sounds like you won't be convinced without an official reference either, but I agree with your coworker. There is no valid rule that says that only sentient beings can have a possessive. com/2009/02/23/preposterous-apostrophes-viii-inanities-in-inanimate-possession / If you google inanimate possessive , you'll find many more.
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AnonymousFor example, instead of saying "the instructions for Form x" he'll write "the form's instructions". Or instead of saying "the contact person on the form" he'll write "the form's contact person". He doesn't agree that this sounds odd in formal writing and he thinks my way sounds odd and too proper: "the instructions for the form" or "the contact person on the form