What I was really interested in was a CS where I could buy a drink--just the empty cup--but be able to refill it as many times as I want while I'm eating my meal in that restaurant.
But I was there today, and this doesn't seem to exist. All the cups have chips in them that limit you to filling the cup once only. The Coke Freestyle program is just as you stated,
@andrniki. I asked the lady working the counter if there were any parameters regarding the "extra days," as in if it all needs to be in one visit--like Disney popcorn buckets--or if, as an AP holder, I can just bring that cup back anytime and pay the $8.99 plus tax, minus my 10% annual passholder's discount. She said I could use it any time, and reminded me to be sure to reactivate at an actual restaurant rather than a kiosk, so I get my AP discount.
I probably won't always want to pay close to $9 to drink all the beverages I want for one day, but there will be some days this summer where I'm sure I'll be glad to. I always carry a backpack so I don't mind throwing the cup in there.