Matsumoto–Ohno interpolation conjecture for face hypergraphs of planar triangulations

Let $H$ be a $3$-uniform face hypergraph obtained from a planar triangulation. A coloring of $H$ is complete if every pair of colors occurs together in some hyperedge; write $\chi(H)$ for the chromatic number and $\psi(H)$ for the achromatic number of $H$.

Matsumoto–Ohno conjecture. If $H$ is $3$-colorable, then it admits a complete $t$-coloring for every integer $t$ satisfying

$$\chi(H) \le t \le \psi(H).$$

The conjecture proposes the interpolation property for complete colorings in this special family of face hypergraphs. The source states that it is disproved in the paper by a particular hypergraph of order $12$.