Good news -- the insurgency is over! Now we need a new strategy for the Iraq War.

[Fabius Maximus]

Your question goes to the heart of the issue.

Wikipedia:

An insurgency, or insurrection, is an armed uprising or revolt against an established civil or political authority.

My dictionary:

insurgency: an organized rebellion aimed at overthrowing a constituted government through the use of subversion and armed conflict.

This op-ed gives is a syllogism. Perhaps two (loosely defined).

1. There is fighting.
2. There is no established national government.
3. Therefore the fighting is not an insurgency against the national gov't.

Here is the second one.

1. There are legitimate local governments in some parts of Iraq.
2. A national government must either have legitimacy or be composed of parts that have legitimacy.
3. Therefore the Iraq’s local governments are the basis we should work with to build a federated Iraq state.
4. Let’s stop attacking the militia and attempt to cut some deals.

Nothing original in these. These things have been said with increasing frequency during the past year. Perhaps this just frames the arguments a bit differently.