[CharlesWayneCT]

The National Guard Ballistic Missile Defense Mission:

This thesis examines the American defense policy decision to assign the Ground-based Midcourse Defense (GMD) portion of the Ballistic Missile Defense System (BMDS) mission to units of the Colorado and Alaska National Guard.

You are probably partly right that the terminology used (anti-nuclear missile battery) is faulty.

But the Alaska National Guard does have a direct role in the defense of our country, is on-guard 24/7, and IS under the command of the Alaska Governor, Sarah Palin.

So she DOES have control over part of our country's defensive missiles.

[ROLF of the HILL COUNTRY]

I couldn't access the website you linked, so I can't tell if this is current or (as I suspect) future assignments. The only ABM system that we had was stationed around Minot AFB. To my knowledge, we still do not have any portions of the new, multi-layer system operational. The excerpt says it will examine the “defense policy decision”. That does not mean they are deployed yet. The decision may have significance in the design/deployment location/cost of the other portions of the total system, and is part of the design process for the BMDS.
The National guard units on active duty status, whether Air Force or Army, fall under their MajCom chain of command starting at the POTUS. The Governors do not command them while they are active.