Inside Bright Hope Baptist Church, the luminaries of Philadelphia’s black political world gathered for the funeral of former Representative William H. Gray III in July. Dozens of politicians — city, state and federal — packed the pews as former President Bill Clinton offered a stirring eulogy, quoting Scripture and proudly telling the crowd that he was once described as “the only white man in America who knew all the verses to ‘Lift Every Voice and Sing.’ ” But it was the presence and behavior of Hillary Rodham Clinton that most intrigued former Gov. Edward G. Rendell: During a quiet moment,...