The eventual junction-occupation conjecture for optimal polygon fillings

Let $G$ be the polygonal domain under consideration and let $M(G)$ be its medial axis, including its junction points. An optimal filling solution is a filling by $N$ discs maximizing the paper's filling measure.

Eventual junction-occupation conjecture. For a given $G$ and $M(G)$, there is an $N'$ such that for $N\geq N'$, the junction points are always occupied in the optimal filling solutions.

If true, sufficiently large optimal fillings would occupy every junction point. The supplied text uses this claim to justify eventual self-correction of the heuristic algorithm, but provides no proof or resolution status.