With nearly 8 decades of misspent life behind me, I have concluded that nothing is "impossible" any more; however, lots of things are highly improbable - - a 3-year old starting up and/or taking off on an F3 Spyder alone, all by herself, is one of them.
We can all conjure up our own speculative scenarios. The only one that will count (truthful, fictitious or otherwise) is the one which the legal 'spinners' manage to convince earthbound authorities should prevail. Perhaps only God really knows (if you're a believer).
If I had to speculate, it would go something like this: Dad's out riding; looks like his mount is a fairly recent F3. He's proud and happy, and being admired by kid(s). In a moment of misguided enthusiasm to turn this into a 'parental teaching/learning experience' with young daughter, he decides to let her learn what it's like to be a 'big person' and share the fun. He's already on the F3; he picks up child and places her in front and astride the gas tank, where she can reach the bars. Perhaps he starts off, gets it rolling. At some point, she is allowed/encouraged to put her hands on the grips. "You drive it, honey". He removes his hands to make this possible. The kid is coaxed to twist the throttle. However, with no real sense of what it does, and no ability to comprehend the power of the 'beast' she is now in charge of, the unfortunate (but not unexpected/unforeseen) result occurs. She twists; the Spyder surges forward. She panics and grabs the throttle even tighter, causing it to twist even more. The Spyder accelerates even faster. Dad, who has his hands in the air is thrust backward with little to hang on to, and eventually slides off; the kid, hanging on for dear life to the throttle bar, and reaching as far as her little body will allow, eventually falls off. The unmanned Spyder continues until its demise. Or something along those lines. In short, my 'theory' is the parental 'show-off/give the kid a thrilling experience' format gone awry. I simply don't buy into the suggestion that "somehow the kid did this on her own" or that there is some manufacturer or product liability failure. While acting with every 'good' intention, people (including parents) can do stupid things.
It reminds me, chillingly, of the day I watched a brother-in-law put a loaded revolver in the hands of his 3-year old son, my nephew, while shooting target practice in our farm yard. His reason: he "wanted to teach the kid about guns and safety", and show him what it was all about. Insane; expecting that level of comprehension from a 3-year old???!!! (I could add, btw, that this same bro-in-law later shot himself in the leg while in his pick-up playing with that same gun; did someone say 'poetic justice'?) Same for trying to give a little kid a Spyder-driving lesson at the controls. Take 'em for a ride, sure - slowly, safely and strapped in. But not at the controls, please. And no conjured up excuses for plain adult stupidity; Pretty Please. And, yes, thankfully no serious injuries, especially for the innocent 3-year old.