Personally, I don't even trust runDisney and always plan to be a self-sufficient as possible.
During my first Dopey, they were out of bananas by the time I got to the first banana stop (which probably started some of my underfueling issues later in the race) and at the next aid station they were out of Biofreeze. This past year, they didn't have anyone available to refill personal water bottles and I had to eventually take multiple cups to do it myself. Everything eventually worked out in each case, but I'd rather have a plan in advance than be wasting brain cells that I don't have figuring it out on the fly.
A secondary benefit is that this gives me the ability to help out other runners too. I've been able to pass out packets of Biofreeze (I always carry at least one) and fuel to people who aren't prepared when the race lets them down. I was running with someone at a local half recently and she asked if I was always a "running mother." Well, yes, I guess I am.
(And sidenote - reminder that Disney has bottle refilling stations near a lot of the bathrooms in the parks. I found them afterwards.)