Two things, both happen to be personal experiences from my family:
1) I was 8 or 9 and my sister was around 2... my parents had the bright idea of bringing one of those harnesses on a leash for her, because she was full of energy and was the kind of kid who couldn't stand to be in a stroller if she wasn't napping. The leash thing seemed to work fairly well, and my parents brought a stroller as well so that she would be able to nap as needed.
Anyway, we went to the Japanese place at Epcot for dinner one night, and my sister had apparently figured out how to escape from the harness. Before my parents knew what had happened, we heard screams of "catch that baby!"
As we looked towards the kitchen, where the screams had originated, all we could see was her blonde hair and giggling face as she came running out of the kitchen with several cooks and servers behind her.
2) This may have been on the same trip, but I want to say it was a couple of years later... we were waiting in line to meet a character (it was someone who was a little less prominent; I don't even remember who now to be honest... maybe a pirate from Peter Pan?). My sister, who was somewhere between two and four at the time, walked right up to him and asked him, "will you please sign this?" He looked at her autograph book, looked at her, nodded, and scribbled the word "this" on a page in her book and gave it back to her. I thought that was hilarious at the time, but my mom was pretty upset.
I have to admit... I still giggle when I think of that.
ETA: I admit those aren't really "outrageous" but figured they were worth sharing nonetheless.