Yes, I think skewness could add the possibility that all 4 of your |||| cells could have face adjacent faces to the COI (but still possibly none of them could be) and in this case you have shown that we are seeing a pentahedron.
EDIT: I think the only way to say for sure that all 4 of your |||| cells are adjacent cells would be if the definition of adjacent cells includes faces with common edges…
To continue this discussion I think we need an answer on what does adjacent cells mean?
Which brings us back to which of the 7 permutations of pick 1,2 or 3 of common faces, edges or corner points, is the meaning of cell adjacency (especially WRT our volumeRatio)?
EDIT: If the adjacent cells definition includes all permutations, then an internal hexahedron cell (not touching the geometry or BMB surface) would have 26+ adjacent cells (I am not sure what the upper limit would be and I am not sure we need to know ). Sometimes I have trouble saying what my brain sees