You missed an important phrase about the nose push maneuver: "With tiger sharks..."
That suggests likely species differentiation.
Great Whites don't seem to follow the same rules since people studying them are pretty much always seen in metal cages to protect themselves. That nose maneuver might end with a missing arm.
And then you have nurse sharks. You can avoid attack from them simply by not threatening them first.
act as a predator, not as a prey
face the animal, keep eye contact, and push down on the nose