As the coronavirus epidemic spread around the globe, the Centers for Disease Control and Prevention provided restrictive guidance on who should be tested, archived pages on its website show. While agencies in other countries were advising and conducting widespread testing, the CDC, charged with setting the U.S. standard for who should be tested for the virus, kept its criteria limited.

A botched initial test batch also meant that tests were slow to be distributed and in short supply. Now, the Food and Drug Administration...