Yesterday, a notification popped up on my phone. “Traffic to your website has increased by 600 percent,” it said. I opened an app that can show visitor data, and, sure enough, the number had skyrocketed. People were stopping by from the UK, Russia, Nigeria, the Philippines, Finland, Liberia, Sweden, and dozens of other countries. It could only mean one thing: the story I’d recorded here in Seattle with BBC Outlook had been broadcast around the world.

Two weeks ago, at KUOW public radio in Sea...