If you point a gun a me I have the right to shoot you dead in self defense. I don't have to worry about your state of mind. And I don't have to get a court order allowing me to shoot you dead.
If the facts and circumstances (like I'm living in a foreign country, I'm a member of Al-Qaeda, I'm a member of the hierarchy of Al-Qaeda, I've repeatedly encouraged and participated in attempted attacks on the United States) the U.S. government has a right and duty to do what is necessary to defend the American people. These facts are somewhat different than someone just peacefully going about his own business. If you don't see that I'm sorry for you.
Al-Qaeda doesn't advertise its membership, it engages in security measures to conceal it, so your hypothetical is foolish in the extreme.
“Al-Qaeda doesn’t advertise its membership...”
In a way, they do. However, by the time credit is taken for one its member’s suicide bombings, they’re out another member.