Sadly, infant injuries and deaths have not been zero. There is a reason the NTSB wished to have the rules changed. I researched the topic and found several incidents of lap children, both belted (tethered) and unbelted either being seriously injured or dying during accidents or severe turbulence where everyone else survived or were relatively unscathed.

I did this research after a Lufthansa crew insisted that I install the car seat facing forward with my newborn in it. Anyone with children these days knows that is absolutely wrong and dangerous, and that infant car seats should always face rearward, even on an aircraft, per manufacturer's instructions (until they reach a certain size/age, but certainly for young infants). The FA's reasoning was that all passengers must face forward for take off and landing. Because it is impossible to properly secure the seat facing forward and the fact that it would cause serious injury to a fragile newborn in the event of an accident, I refused and the FA took away the car seat and gave me one of those infant belts that loop onto the adult's belt to use instead.

Lufthansa later apologized, but this goes to show that Flight Attendants are not all-knowing, even when it comes to their own airline's rules, and they are people too, and they can lie. In the case of this Canadian singer, other passengers back up her version of events. None have come out to back up the FA's version having the kid running wild in the aisle.