All I remember of Jack White was a show he did on "Badge Man" (along with Gary Mack), where they got a very fuzzy shadow on the grassy knoll, not very convincing photography, it seemed more like seeing patterns in clouds.

That is correct. White went into the darkroom and kept englarging and contrast enhancing until something suspicious-looking formed. At the tiny scale of the "Badge Man" image, most of the detail (in the sense of sharper features) you see is photochemical and not optical. Seen in context at normal scale and contrast, that area looks no different than any other part of the tree.