Place the midline so that lattice point is on center (so the center of the tree lies on the line of sight). Now shift the strip so that the center of the tree barely hits the strip. Then the center line is indeed occluded. But there are lines of sight, within the strip, that are not necessarily occluded (shift your eyes a smidge off the center line, away from the side hitting the tree).
Stated slightly differently, there is no guarantee that a tree is centered on every line of sight (and indeed that cannot happen with a lattice). The Minkowski guarantee is that a tree center exists withing each visibility strip. Not the same thing.
