The Arizona Game and Fish Department press release:
Mountain lion incident in Madera Canyon offers lessons for public
Animal killed in popular recreation area after aggressively stalking hiker
TUCSON, ARIZONA – An unusual-acting mountain lion that had been stalking a hiker and his dog on Saturday in Madera Canyon in the Santa Rita Mountains was located and killed by the Arizona Game and Fish Department on Sunday, Oct. 26.
“This strange-acting mountain lion posed a clear public safety threat,” said Leonard Ordway, the Tucson regional supervisor for the Game and Fish Department.
The mountain lion not only stalked the hiker and his dog, but it continued to act aggressively toward the hiker even when the person tried to scare it away.
Ordway said that the hiker did the things he was supposed to – he shouted and tried to make himself look bigger by waving his arms, he picked his dog up off the ground, but the mountain lion continued to approach. The hiker then used his pistol to fire two warning shots, and the mountain lion continued to approach, at which time the hiker shot directly at the lion and the animal finally ran away.
Authorities tracked it down and killed it, presumable with a firearm of some sort.

Worst Case Scenario?
The press release then lists a total of 13 “safety tips for anyone who encounters a mountain lion or other large predator.” Interestingly, not one of the 13 says anything about a gun.
A story in which the hiker “did the things he was supposed to” but only ended the threat when he shot at the animal doesn’t even mention using a gun to protect yourself.
Only one tip says anything about defending yourself:
Fight back if attacked: Many potential victims have fought back successfully with rocks, sticks, caps, jackets, garden tools and their bare hands. Since a mountain lion usually tries to bite the head or neck, try to remain standing and face the attacking animal.
As I wrote in 2004 in response to a California statement which reads suspiciously similar to this Arizona statement:
That’s not fighting back, that’s a desperate last-ditch attempt to continue living.
Pulling a gun and blowing the damn thing away is fighting back.