Anthony was introduced at a standing-room-only press conference with his wife, the former MTV personality Alani "La La" Vasquez, and the couple's son, Kiyan, now six.
As Mr Alani puts it, the network differs from all other militant Islamist movements in its global reach, its focus on very high-value targets and its skill at covering its traces by spiriting agents from one country to another.
The very fact that the eight people detained in Madrid stayed in one country Spain most of the time suggests that they cannot have played a central role in the network, according to Mustafa Alani, an associate of the Royal United Services Institute in London who has been studying al-Qaeda for many years.