The driver of a car is responsible for what happens when a car is in motion. It doesn't matter if that person runs through a stop sign or is speeding and rear-ends someone or simply hits the gas pedal instead of the brake. When this happens they are at fault.
In Florida, this type of accident is a lot more common then you might think. They are pretty common for drivers under the age of twenty and those over the age of seventy. When someone hits the gas by mistake instead of the brake pedal, the car usually travels a long distance at a rapid rate because the driver panics and doesn't pull their foot of the gas fast enough.
Regardless of how the driver makes a mistake in Florida, it's their responsibility to control their car.