They forget one of the safety measures:

a sidearm with a caliber beginning with '4' when in lion territory.
“I don’t know why, I just started singing opera really loud,” Koestonsky later told KUSA. “It kind of put its ears down and just kept looking at me, and it sort of backed away. Then, it came around the bushes an came towards me again and crouched about 10 feet away.”

Although the singing did not repel the animal, it may have deterred the mountain lion from directly attacking the hiker. Koestonsky said that the large cat alternated from grooming itself, pacing, and following her. At one point, the mountain lion was a mere eight feet away from the hiker.