Who said anything about:

... dismissing it ...
Did I ? No I did not.

I did answer your question - admittedly addressed to Bob, which was:

Bob - strongly agree with your points about the difference between legal legitimacy and political legitimacy. Will be very interested to hear whether you think that difference is adequately reflected in the document.
JP 3-24 does not use the term "legal legitimacy" once; it uses the term "political legitimacy" twice - here are the snips:

I-6 ... Political legitimacy of a government determines the degree to which the population will voluntarily or passively comply with the decisions and rules issued by a governing authority.
II-9 ... Revolutionaries often want to change the fundamental sources of political legitimacy around which government and political authority are organized.
The rest of the monograph otherwise uses the unmodified word "legitimacy" 134 times, without guidance as to whether that word means "political legitimacy" and "legal legitimacy".

So, now, to answer your question again: The difference between legal legitimacy and political legitimacy is not adequately reflected in the document.

Or, perhaps, I'm to assume (which I won't do) that "legal legitimacy" is equated to "rule of law" (used 20 times). Thus, is this also the "definition" of "legal legitimacy" ??:

III-3 (3) Rule of Law. Access to effective mechanisms to resolve disputes without resorting to violence and in accordance with a consistent set of rules is fundamental to ensure that the population feels secure. The rule of law should govern the conduct of COIN forces, transparently and consistently following its own rules to demonstrate the political credibility of the HN government and its allies to the population and the insurgents.

(4) As with governance systems in general, the legal systems deemed most
effective and legitimate in the eyes of the local population may differ greatly from Western models, and may vary across the operational area (e.g., the capital city versus remote rural areas). JFCs should endeavor to support locally appropriate systems while adhering to US and international human rights standards.
Answer that and, perhaps, Bob or I can go on; I say "perhaps" because the term "rule of law" is an arguable point, to say the least. For your reading pleasure (both from the Mansfield Center), The Rule of Law: A Lexicon for Policy Makers (2000); and The Rule of Law: Perspectives from the Pacific Rim (2000). Politics (often very local) and popular culture (again often very local) are more important factors than law in popular insurrections.

Regards

Mike