The dining plans include a non-alcoholic fountain drink (e.g. soda, coffee, tea, lemonade). At some of the Disney owned restaurants you can get milkshakes, smoothies, or virgin cocktails - ask first. At the non-Disney owned venues they are much more strict because they are reimbursed according to the limitations of the dining plan so only the fountain drinks are allowed. Alcoholic drinks and drinks in souvenir cups are excluded at all venues.
I imagine in the trip reports the OP was reading they were refering to alcoholic drinks or specialty beverages for which they had to pay OOP and thus had to pay tax as well.