I think that there are aspects of Kaufman's work that represents verbatim theatre.  The most notable of this would be the collection of interviews from people in Laramie and the interviews of the members of the Tectonic group themselves.  This represents verbatim theatre because of its docudrama style, allowing the voices of the people in the setting speak for themselves.  This also represents verbatim theatre because it allows for a type of historiography present in the way in which interviews are collected, marking primary source footage in a secondary source element.  Where I think that Kaufman's work might deviate a bit from the verbatim format lies in how the work presents life in Laramie and Matt Shepard's life, in general:

In order to accurately present the information that he and his troupe had gathered, Kaufman created the illusion of reality by formatting his play not as a fictional story, but rather as a reenactment of the interviews. The fictional, or artistic, part of the play was in how Kaufman pulled all this information together and made it tell a story.

It is here where Kaufman differs from true verbatim style, which is more concerned with a historical recreation.  Kaufman wants the political message of his work to have the greatest effect.  This means that the construction of Matt Shepard's experiences and his life in Laramie is done to facilitate a larger discussion of homophobia and fear of "the other."  Verbatim theatre is more concerned with this recreation, whereas Kaufman's work seeks to start a much needed discourse.  This is why specific parts of the work can move away from verbatim style, as Kaufman seeks another form while embracing aspects of it.