[dragonwriter]

> Given that the US military has killed nearly 4,000 people with drone strikes in Pakistan over the past decade, a country in which no formal military conflict exists

Pakistan is a country with which no formal military conflict with the US exists, but it is not one in which no formal military conflict involving the US exists.

The 2001 AUMF is a (ludicrously open ended) conditional exercise of Congress' Constitutional power to declare war, and the parties targeted in Pakistan are parts of groups to which the executive branch has determined that the conditions in that act apply.