Same cats, wejo. I've had them in my yard in Scottsdale and faced one down in Cave Creek before. They definitely have them in Flag as well along with black bears which I've encountered while running around Humphry's. Black bears are really no big deal though unless it's a mom with cubs. The dive down I17 is by far and away the most dangerous thing around.
Felt the same thing running/hiking in Montana with respect to the grizzlies. There's a ton of arguments on both sides of the dog protection debate. My thought is that a dog would be good to have provided it doesn't wander off and attract bring the bear to you and is able to remain calm/obedient in a confrontation until told to go. In other words, a well trained dog.