To get free valet parking, you have to eat at the hotel’s restaurants.
You can’t show a receipt from Brown Derby to the valets at Boardwalk and park for free.
DT, unless you’re a Florida resident, you can’t get a TIW membership, so free parking is generally a moot point at the parks. I don’t know if Florida resident TIW members can park for free at the parks and I know that the toll booths are not connected to the dining reservation system so that they can check if you have a reservation. With valet, they take your car and you don’t pay until you claim it. That’s when you show the card and the receipt.
I’m not saying you don’t get free park parking outright with just a TIW card, I’m just saying it isn’t logical.