LOUISVILLE, Ky. — Kim Davis’ lawyer stood onstage in a Washington, D.C., hotel and pointed to a photo on the screen. It showed 100,000 people packed into a Peruvian soccer stadium, Mat Staver told the crowd, to pray for the Kentucky clerk battling gay marriage. The crowd erupted. It wasn’t true. Staver’s firm, the Liberty Counsel, which revealed Davis’ secret meeting with Pope Francis, has been accused by advocacy groups of peddling misrepresentations in the past.