Let's just state the obvious right off the bat: A pedal car is not a real car, and it should never be on a real road. It's a little car with a little kid in it. Not even the driver of a tiny smart fortwo car is going to be able to see a pedal car on the street. That's the very definition of accident waiting to happen.
You should also be aware that the brakes are straight out of a "Flintstones" cartoon.The bottom of a pedal car is wide-open, and your kid applies the brakes by just putting his feet down. However, unlike Fred Flintstone, your kid should be wearing shoes with grippy rubber soles for safe braking — not barefoot.
When a pedal car flies down a hill or is pushed really fast, the wheels move the pedals faster than a kid's legs can manage. The problem is that those pedals become an egg beater, winding your kid's shoelaces, jaunty silk scarf, or any other dangly bits in the mechanism. The pedals can also beat her shins up pretty badly, which makes for a terrible video to post on Facebook. Just keep the pedal car on a flat-ish surface and don't tie it to the bumper of your truck, and she's good to go — at a nice, slow, preschooler-appropriate pace.
If you're really looking for a reason to say "no" to a pedal car, Grinch, then there have been recalls of steel-bodied cars in the early 2000s for having lead paint. But that was just one company, and it was more than a decade ago — things seem to be fine since then. Finding statistics to back up your weird pedal-car phobia will be tough; most hospitals lump pedal car accidents in with bicycles and tricycles for injury reports. There are a lot more kids on bikes than there are kids in pedal cars. Those two-wheeled demons are responsible for most of the emergency room visits. Finally, if your heart grows three sizes that day, and you do decide to buy your Cindy Lou Who a pedal car, you could always teach her proper hand signals for stopping and turning.