Not in the least. The best way to avoid GI upset is to scrupulously wash your hands
Dilution is the solution to pollution is what we were taught in Micro. Dilute out the bad guys, copious amounts of water will go a long, long way! I carry baby wipes because germex is fine, but I like to get the grime off.
It's not just disney, it's anyplace . And NO, I don't really get too concerned...common sense goes a long way . For example: You taste a piece of salmon, it tastes "off". Quite simple: Don't eat it!! These things happen. You just have to be conscious....Wash your hands, and hopefully the kitchen staff does the same!
I'm more concerned about samonella (spelling?) than anything else... I suffered a horrible bout of food poisining a few years back (NOT at disney, here in NY) from a bagel place...it was very humid, and the four people out of 11 that got sick, were the only ones that ate the Vegatable cream cheese... It does cross my mid anytime I eat out, and not just at disney, but I wouldn't worry too much about it.
Had
Salmonella...in the hospital for one week and I'm hardly a wilted violet...pretty sturdy and it dropped me like a fly. Oddly, I've also worked in a micro lab and never caught a thing! I washed my hands like a fiend!
A large number of people go to WDW, their numbers of food borne illness don't seem disproportionately large, however. Any food prepared by someone who did not wash their hands properly or food prepared using unclean cooking utensils, cutting boards, or other tools, dairy products or food containing mayonnaise (such as coleslaw or potato salad) that have been out of the refrigerator too long...frozen or refrigerated foods that are not stored at the proper temperature or are not reheated properly, raw fish or oysters, even raw fruits or vegetables that have not been washed well. WASH YOUR FRUIT! Raw vegetable or fruit juices and dairy, undercooked meats or eggs, water from a well or stream, or city or town water that has not been treated ALL increase your risk. That said,
you could easily be fine as well. The thing is care. Would you grab an apple at home and not wash it...then, I wouldn't do it at Disney or the Grand Canyon or NYC or wherever. I don't order rare burgers, ground meat is tricky. I do order med or med rare steaks because the type of meat is different. One piece, not ground, hot in the middle.
Food poisoning onset varies with the type of culprit. Most common food poisonings, Coliforms/Staph usually within about 4-6 hours of eating. Salmonella can be up to 72 hours after, Norovirus within 24 hours, usually. BTW, had that, too, and it would bring a Clydesdale to it's knees! You could easily have the bug in your body before you even stepped foot on WDW property dependent on the organism. Air travel is as easily a culprit. Food poisoning is very abrupt and very "IN YOUR FACE" if you know what I mean. The onset is quick and dirty.
The thing people don't do is hold off on food until the "symptoms" (ie., diarrhea) have passed, no pun intended. Don't eat dairy, stay away from hard to digest foods for 24-48 hours. Go for cereal, rice/grains, potatoes, pasta...and drink lots of plain old water. Don't grab the Immodium right away, let the beast clear your system. Immodium stops it, yet, but it's still there...and can come back with a vengence when you quit taking it.
I wouldn't be fearful...I think diligent or conscientious is a better word, but that goes for anywhere, not just WDW. I do not think WDW is a den of food poisoning iniquity anymore than anywhere else.
p. s. I don't like public drinking fountains...just me.
I drink a LOT of water, so that might be why...just the change of water. I now drink bottled only when I go, and I have noticed a decrease in stomach issues. 
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