Possible cooked S-boxes in Kuznyechik & Streebog..Russian cipher & hash

The sentence which seems critical in his posting is maybe this one: Arnaud Bannier proved in his PhD (see also [3]) that an S-box preserving a partition of the space into additive cosets in such a way that it interacts with the linear layer was necessary to build some specific backdoors.

I am not a cryptographer or a mathematician. These words do seem very worrying to me. He seems to be saying the primary quality, the preservation of a property across sbox and linear layer was demonstrated.