I know our water here at home goes in cycles depending on the weather. Some days the water from the tap isn't too bad, others it's downright dreadful. That may be the case in Florida as well.
When we were there in August, the 95º heat wave drove me to more than one water fountain. Usually, I avoid Disney water fountains because of the taste. This time, however, I really didn't notice it. Perhaps they were having a good week, perhaps I was so hot any water would have tasted good, or perhaps it's not the issue it once was.
We packed our Brita filter with us and used that to fill water bottles every night. That water tasted just as good as the bottled water. Unfortunately, there's a tradeoff between how much you want to carry around, and how long your own water supply lasts in the parks.