For more than a half century, residents of a tiny western Mississippi community have counted on Dr. Carrol Landrum’s house calls for their health care. The sight of Landrum’s dented, black, 2007 Toyota Camry pulling up has brought relief to countless shut-ins in Edwards, a town of about 1,000 about 28 miles west of Jackson. But the state medical board is probing the country doctor, an 88-year-old World War II veteran, because, he says, they don’t like him working out of his car. “I didn’t know there was any law against it,” Landrum, who grew up in Taylorsville, but has...