The oath referred to is that swearing fealty to Al-Qaeda and Osama bin Laden. Abu Jandal, who served as the leader's bodyguard from 1996 to 2000, took the oath. His brother-in-law Salim Hamdan, who worked as a paid driver and mechanic for the group, didn't. Hamdan ended up in Gitmo; Jandal ended up on TV, giving interviews to 60 Minutes and Al-Arabiya about his days with OBL.
You might recognize Hamdan's name from the landmark 2006 Supreme Court case Hamdan v. Rumsfeld, which declared unconstitutional the Bush administration's high-handed approach to trying accused terrorists. Laura Poitras's complex documentary takes up the story as Hamdan is hauled before a military tribunal on new laws drummed up by Congress especially for his case.
The film intercuts that trial with Jandal's guilt-ridden reflections while he drives a cab in Yemen; the result is compelling both as drama and as an indictment of the eight years of folly known as the War on Terror.