The removal guy said in a later interview that most of the bees in Arizona are Africanized. The swarm he removed had “bedded down” for the night and were mostly docile at that point. He said a problem could occur if the net or the swarm were hit with a baseball or other object.
Bees are about the only critter I worry about when I'm out hunting or hiking in Arizona, much more than rattlesnakes. I've heard that Africanized bees will chase a person for up to a mile, and there's no way I could run a mile in the desert these days. If I notice more bees around than usual, or if I hear the sound of a swarm, I leave the area cautiously and quietly.
A local beekeeper once told me that Africanized bees have a warning behavior of bumping into intruders before attacking, so if you have bees flying into you and bouncing off, get out of there. Don't swat them, because a dying bee will release pheromones that will trigger an attack by the rest of the bees.