I've never had a problem getting the large sized bottle of water with my cs meals. I can't specifically remember how it worked with my dd, but I do know I don't let the kids drink soda during the day at WDW (too dehydrating) and they always had either milk, juice, or bottled water. I didn't pay OOP for anything, so maybe it's just the place you go? We usually eat counter service at Pecos Bill's, Columbia Harbor House, Flame Tree, or Sunshine Seasons along with various resort food court locations.
I do not drink, nor do I let me kids, drink tap water from WDW. I find the central Florida water is rough on our tummies (have no idea why) so it's strictly bottled for us.