It sounds like the DVC CM was confused

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Free parking at the theme parks is included w/ a stay at a WDW resort including DVC resorts at WDW. So if you have registered guests staying w/ you in your WDW villa they should be able to verify that they are staying at a WDW resort w/ the theme park parking booth CM via their MB or phone or room key card - whatever they’re using to open the villa door - for free parking when they enter a park’s parking lot. It’s just like they’ll scan MB/phone/key card to get into a park half an hour early for EMH or scan to get on rides after park closing during evening EMHs.