8 Years ago I worked as a contractor for WDW. One day, me and a CM had to go visit our back-up "puter" which was stashed down in the "security central" area of the tunnel.
We walked in to the tunnel as many CM's were getting ready for the afternoon parade. The guy playing goofy had was standing 10 feet from us and had his head off. He was a 6' 4" brute of a guy. Unshaved, looked stoned, etc.
The CM I worked with leaned over and said "that is the guy that will hug your little girl in the park tomorrow!". It was very funny.
What I can say from my experience is that WDW takes this type of incident very, very serious. To that end they have tons of camera's and a large number of under-cover security agents in the park.
Unfortunately, in this day and age something can happen any time any where. And, no company can have eyes everywhere. But, from my personal experience I believe my daughter is safer in the MK then at any mall.