As a non-native Floridian, I also do not drink the water! However, you are usually exposed to multiple types of water while in WDW, and other parts of Florida. The tap/shower water is from the aquifer, which (as already stated) is hard water (that's been treated), and also has a slight trace of sulpher in it (hence the "funny smell") The water generally used for watering lawns, fountains, etc. is from shallow wells. It has a lot more sulpher in it, so has a very strong (and to me, unpleasant) smell, and will stain buildings yellow! It appears that most places like WDW treat this water before using it (but not private homes & smaller businesses), but it really isn't potable. Then you have "natural" water sources, like rivers, lakes, and the ocean. They can all vary, from the crystal clear spring fed rivers , to the tannic, brown colored rivers and lakes, like the St. John's and Bay Lake. They also can have varying bacteria, etc. levels, so can possibly make you ill if swallowed, even accidentally. And of course, salt water is never potable in it's natural state.
I don't like the flavor of most tap waters, so always drink bottled. I've also found that the tap water does vary from time to time; sometimes it does smell like I'm showering in poolwater, other days it's not bad. I assume there are many factors influencing this...perhaps you were there during a drought, then came back when water tables were back to normal.
What I'm saying is, you could all be right!! I suspect that sometimes the water does smell/taste bad, and other times you might not notice it!
And I'm sorry about your daughter's reaction! I would not even attempt to speculate on the exact cause!
I will mention that the last time we ate at RF in AK, my daughter had a bad reaction to the rainsticks...I hesitate to say food poisoning, but the timing was correct if you follow my drift!
(and no one else got sick, so it wasn't the water)