That diagram represents a length of 2, not a length of 3, see? Here's three:
X--X--X--X
0 1 2 3
It's not that the hazelnuts are somehow imperfectly laid out or are an imperfect representation. It's wrong in principle, not practice (I mean it's wrong in practice too but every representation is).
You didn't miss it. You were focusing on the lattice edges, and PP was focusing on the lattice points. You're both right (except for PP's "No!" which should be "Yes!").
