IMO, I think that the mystery person had sinister plans from the get go hence why she wasn't picked up at the airport. The park may have been a normal middle meeting ground for her in the past ( or the like) and she didn't think anything of it, but I think the person had an agenda all along.
Where would said person take her? Their private cabin, boat, or was it more immediate where he alluded to a destination and ended up on a back road, woods, fields etc? Are there areas like that close by? I know the highway is right there.
Sorry, this is where my mind has been. MOO