That's anthropomorphism.
Dogs don't need some long, heartfelt apology. They're pretty good at understanding humans, they've been around us for millennia after all, and most people instinctively know how to convey to their dog that they're not being aggressive - the dog quickly understand it was an accident.
The big apology, the tears, etc that's for us, to make us feel less bad about having hurt them. They don't need it, but they will gladly take the cuddling and petting, so no harm there. :)