To rudely interject into this debate with a straw-man argument of my own...

How about viewing this argument as a framework whereby government policy is set/translated into the levels discussed:

- Strategic Policy (how AfPak is to be shaped IOT disrupt violent extremism, deny AfPak to AQ and stabilise the Pak nuclear capability)
- Operational/ Theatre-level Policy (conduct a COIN-based campaign around the key pop centres while conducting FID IOT achieve transfer)
- Tactical Policy (ROEs/ Clear-Hold-Build process/ priorities on minimising civ and FF cas)

Military forces are only ever able to operate tactically, but the tactical effects can be in support of either strategic, operational or tactical policy depending on their employment, task, etc.

Viewing the three 'levels' of war as distinct elements of policy-making, rather than a physical level in which one functions, seems to be an elegant solution to some of the points either side of the debate.