It may have just been a reception staff member unfamiliar with the benefit. Alternatively, it is possible that if a property offers both self-parking as well as valet parking, the self parking will be free, not the valet.

If it were me I would just use the valet service and if they still end up adding a parking charge to the folio, I'd just ask the Globalist line or my concierge to have it removed.

I didn't really see any full-time valet / bell-hop staff lurking in the lobby whenever I was there, so maybe the front desk fulfills the duty. Plus there didn't appear to be any garage on the small property, so likely parked in a nearby lot or garage.

From WOH T&C:
(j) Free Parking: Globalists receive free parking at participating Hyatt hotels or resorts for nights during which the Globalist stays on a Free Night Award. Free parking benefit is valid at Hyatt hotels or resorts that offer parking, provided that parking charges at such hotel or resort can be billed to the guest room/folio. Not valid at Vacation Ownership Properties. If both are offered by the applicable hotel or resort, benefit is valid for either valet or self-parking. Benefit does not apply to any night for which Globalist is not staying on a Free Night Award (e.g., any paid night’s stay) or any non-stay award redemption (e.g., Dining, Spa, and More Awards).