About one person per month has a reportable injury due to an unfortunate encounter with a garbage disposal. Most years no one gets their fingers mangled. Also, they don't grind your hand to a bloody stump like you'd imagine from horror novels and movies.
The overwhelming majority of these injuries involve fishing broken glass out by hand. A significant minority of them involve dropping the disposal on oneself while installing or removing one.
So no, they're not "perfectly safe" with the power turned off.