People have been seriously injured on even the tamest of rides. There was a serious injury due to a child climbing out of the car on Spaceship Earth at Epcot, a ride that travels at 1-2 mph. Parks certainly don't publicize injuries. I believe that at one time Disney had a policy to prevent anyone from actually being declared dead on Disney property. This included deaths due to natural causes.
However, covering up serious injuries in today's environment would probably be difficult, and covering up a death would be nearly impossible.