Small technicality: I think it's actually the tree radius has to be .16 m (otherwise it might only occlude as little as half of that strip). But very nice in any case.

It is assumed that the origin is the point of vision. In fact any light ray from a outside point to the origin lies (symmetrically in the middle) in a visibility strip. Since any visibility strip contains at least a lattice point at its interior, the corresponding tree occlude the light ray for its size exceeds half of this visibility strip.

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.

The importante fact is that the midline is always occluded by a tree, hence the "eye" located at Origin cannot see the light ray ( midline of the strip) that comes from outside.