The disease investigators arrived at the apartment in street clothes, carrying their gowns, gloves and face shields in Whole Foods bags. They didn’t knock on the door. Instead, they called the resident — a man in his 50s, then California’s first known coronavirus case — by phone. When he answered, he was instructed to move to the farthest corner of the apartment so the team could go inside and suit up. The pileup of samples left the county’s testing infrastructure bottlenecked and on the brink of collapse. A county memo asked hospitals to turn away any suspected coronavirus patient with...