from An Outsider (hey, Canucks aren't outsiders to me )

I was under the impression that as the leader of an organization who had formally declared war on the US, Bin Laden was a legitimate target of any military action that did not violate the Geneva Convention. Does this mean that they would consider it illegal for a spec ops squad to take out any enemy commander in times of war unless you give the poor bastard a chance to surrender?
Your first sentence correctly summarizes the USG legal position as it has been formally presented. Some Obama administration personnel get off that message because they have trouble seeing anything but a "law enforcement" image (i.e., force is limited to defense of self or others in response to a hostile act or threat).

The answer to your second sentence (and question) is "yes"; many folks take the position that response to Transnational Violent Non-State Actors (such as AQ) must be via "law enforcement" rules (capture primary, with kill reserved only for defense of self or others).

The second position is very prevalent in Academia and in many EU countries. An example in US Academia is Mary Ellen O’Connell, the Robert and Marion Short Chair in Law and Research Professor of International Dispute Resolution - Kroc Institute. She is a Vice President at the American Society of International Law and the author of author of The Choice of Law Against Terrorism, 4 J. NAT. SEC. L. & POL’Y 2010. Full pdf at One-Click Download.

Abstract:
The Obama administration has continued to apply the wartime paradigm first developed by the Bush administration after 9/11 to respond to terrorism. In cases of trials before military commissions, indefinite detention, and targeted killing, the U.S. has continued to claim wartime privileges even with respect to persons and situations far from any battlefield. This article argues that both administrations have made a basic error in the choice of law. Wartime privileges may be claimed when armed conflict conditions prevail as defined by international law. These privileges are not triggered by declarations or policy preferences.
Actually, she and I agree on the bolded sentence; except Ms O'Connell has a very limited view of "armed conflict conditions". This is just one example of why, in law, you can't agree automatically to what looks like a good principle. By their works, you will know them.

As to OBL, The Death of bin Laden as a Turning Point, by Mary Ellen O'Connell (4 May 2011) - good statement of her position (contrary to mine). Also read the comments to her article - views at Opinio Juris vary. Her update is summed here, More from O’Connell on bin Laden Killing as Peacetime Use of Force, by Roger Alford (5 May 2011):

The use of lethal force is governed by two types of international law: the law of peace and the law of armed conflict. In peace, international law supports national legal systems when it comes to the resort to force. National systems restrict the use of force to law enforcement authorities — the police, or in special circumstances, the military (I argue here that the SEALs, who are military, kept their use of force at law enforcement levels). Unauthorized persons may resort to force in self-defense if necessary to save a life immediately. Otherwise, using force is considered a crime under international law.

Some crimes are so serious they are outlawed in international law, as well as national law, with the crime of terrorism is a prime example. As an international crime, states around the world have an obligation to suppress terrorism. But in suppressing even the most serious crimes, law enforcement agents must limit the amount of lethal force they use, and excessive force, even in anti-terrorism cases, has been ruled a violation of human rights law by both the European Court of Human Rights [ECHR] and the Inter-American Court.

The ECHR considered a case in 1995 with parallels to the bin Laden raid. In McCann v. The United Kingdom, the court found that members of the elite British SAS used excessive force when they killed IRA members in Gibraltar who were suspected of preparing a bombing. The court found that the operatives should have attempted to arrest the terrorists, instead of shooting them based on intelligence they possessed that the suspects were preparing to use explosives. If the suspects had resisted arrest or attempted to escape, authorities then would have had had the right to resort to lethal force.

This is the law that applied in bin Laden’s case. On May 2, no fighting was going on in Pakistan that would rise to the level of “armed conflict” as defined under international law; Pakistan had to suspend major military operations against militant groups in the country’s tribal areas after the floods of 2010. And despite what some commentators have argued, under international law there is no right to engage in cross-border military force based on the argument that a state is unable or unwilling to deal with the threat themselves. The correct choice of law, therefore, was peacetime law.
No, no, Ms O'Connell - not correct at all; but you believe in what you say. I believe in what I say.

So, choice of law is the argument. What the law is under either choice is actually pretty clear to most folks who have studied it.

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As to the Bear's research project (Title 50), also at Opinio Juris, Was the C.I.A. Director in Charge of the Bin Laden Operation? Apparently so. Does It Matter?, by John Dehn

[Major John C. Dehn is an Assistant Professor in the Department of Law, US Military Academy, West Point, NY. He currently teaches International Law and Constitutional and Military Law. He is writing in his personal capacity and his views do not necessarily represent the views of the Department of Defense, the US Army, or the US Military Academy. The analysis presented here stems from his academic research of publicly available sources, not from protected operational information from, or actual involvement in, aspects of this or any other military operation.]
He does not reach a firm conclusion - work still in progress. And, he noted the importance of our topic here; but alas, did not mention SWC:

The OBL operation is an example of an evolving and unique relationship between the military and the CIA that is, in my humble opinion, under-examined and under-theorized both with respect to the international and domestic legal frameworks and as an element of civil-military relations. Over at Lawfare, a recent post by Bobby Chesney raises intelligence oversight issues about the OBL operation, which seems to me only one aspect of the necessary constitutional/domestic legal analysis. Ben Wittes solicited Mary Ellen O’Connell — twice – for her views on the international legal framework applicable to the operation. Her post below seems to present an implausible view of the attack as a law-enforcement operation. Assuming it is best characterized as a military operation conducted to IHL standards, as Kevin and Michael both seem to agree, may the C.I.A. lawfully oversee it?
He also cites and quotes some specific Title 50 text.

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Ah, the riddle question (as originally stated with emphasis added):

from sw
Could you throw up the definitions of "lawful combatant" and and "unlawful combatant" as used in the AUMF?
Please note and renote "as used in the AUMF".

Let's look (text in Wiki). Gee, "combatant" ain't in the 2001 AUMF. How about that ?

The question often is a debating question - leading to "ain't in the 2001 AUMF; thence, can't be in the rules of situations covered by the 2001 AUMF; hence, you are guilty of war crimes."

Now, there is a link up between the 2001 AUMF (no combatant definitions)and the 2007 Navy Handbook (definitions) - 5.4.1.1 Lawful Enemy Combatants and 5.4.1.2 Unlawful Enemy Combatants. Gee, how could I have missed those sections. Oh, I didn't miss them - I just gave the cites to them, in The Rules - Engaging HVTs & OBL (the OP):

5.4.1 Combatants

Combatants are persons engaged in hostilities during an armed conflict. Combatants can be lawful or unlawful.

The term “enemy combatant” refers to a person engaged in hostilities against the United States or its coalition partners during an armed conflict. The term “enemy combatant” also includes both “lawful enemy combatants” and “unlawful enemy combatants.”

and:

8.2.1 Lawful Combatants

Lawful combatants (see paragraph 5.4.1.1) are subject to attack at anytime during hostilities unless they are hors de combat (see paragraph 8.2.3).

8.2.2 Unlawful Combatants

Unlawful combatants (see paragraph 5.4.1.2) who are members of forces or parties declared hostile by competent authority are subject to attack at anytime during hostilities unless they are hors de combat (see paragraph 8.2.3).
How mean of me to miss the evening feeding.

Whoever is interested in learning something can follow my leads from the AUMF (methodology in a prior post) and come up with the answers.

Regards

Mike