Not to be contrarian, but can anybody point me to the relevant section of the FAA (or UA) guidelines that actually says this?

I looked up the FAA FAR and did a search for "headrest" which came up empty (meaning that term is used in the FARs but not in the context that they have to be down or in any other position for takeoff and landing). § 121.311 (Seats, safety belts, and shoulder harnesses.) and also § 121.317 talk about seats and seat belts and other safety regulations for takeoff and landing but neither mention headrests. I know from other threads that if UA has filed a document with the FAA saying that this is their procedure then they have to follow it. Anybody know where that would be?