Yes, it is okay. We have bought both plastic water bottles and the reusable tin ones and refilled them at either the water fountains or the First Aid center (filtered, cold water).
Food is also okay as long as there's no glass containers.
I always bring in single Cool Aid, Crystal Light, or Ice tea packets, and I go to any counter service who sells drinks and ask for ice water. Its free and you have a free tasty drink It also saves you a ton of money.
We bought some sandwiches at La Brea Bakery last night on our way in to wait for the parade. I was unsure if they were going to let us take them in. No problem!