Distance split tree as the tree of blobs of an equivalent network

Let $N$ be a metric semidirected network on taxon set $X$, let $d_N$ denote its average distances on $X$, and let $T$ be the distance split tree reconstructed from $d_N$. Distance-split-tree conjecture. There exists a semidirected network $N'$ of level at most that of $N$ such that

$$d_{N'}=d_N$$

and $T$ is the tree of blobs of $N'$. This would show that the distance split tree always represents the tree-of-blobs structure of a network with the same average distances and no greater level. The conjecture is motivated by examples and results for non-binary level-1 networks, but the source provides no resolution of the general claim.