The statement is incorrect. A regular
octahedron has four axes, and cross-sections made perpendicular to these axes (through the center) are regular hexagons. The tetrakis hexahedron is a different polyhedron.
The tetrakis hexahedron is a Catalan solid and the dual of the truncated octahedron. The truncated octahedron has 8 regular hexagonal faces and 6 square faces.
The cuboctahedron, a different but related solid (specifically, the rectification of the cube and octahedron), can be described in the context of four hexagonal planes that bisect its interior. It is this related solid that has properties concerning hexagonal planes, not the tetrakis hexahedron itself in the manner described.