Yes, and it is not a slogan. A dull edge needs more force to make the same cut, and it slips off the surface instead of biting in. More force plus an unpredictable slip means a blade traveling fast in a direction you did not choose, usually toward your other hand.
A sharp edge bites where you place it. A dull one skates along the surface until the pressure finally overcomes the resistance, at which point it goes through suddenly and keeps going.
Because you have also applied more force to compensate, there is more energy behind that slip. That combination is what produces the deep, awkward cuts people get from blunt kitchen knives.
A sharp knife cuts you more easily if it does touch you. That is true, and it is why sharp-knife accidents happen too.
The difference is control. A sharp knife goes where you point it and a dull one does not, and control is what prevents accidents rather than what mitigates them.
Keep edges sharp, cut on a board that will not blunt them, and never force a cut. If you find yourself pushing hard, stop and sharpen instead.
See how often to sharpen and safe handling.