During the worst of last month’s wildfires in Northern California, Dick Fredericks got a phone call that passed on “some magical words”: His house was safe.

The message from a private firefighting service hired by his home insurer, Chubb Ltd. CB, -0.12% , was accompanied by an email with some two dozen photos, including one of the service’s firefighters pumping water from Fredericks’s swimming pool to extinguish a brush fire on his Sonoma Valley property.