The original McEliece scheme uses two random matrices S and P to scramble the generator matrix and uses $\mathsf S·\mathsf G·\mathsf P$ as the public key. The Niederreiter variant also does about the same thing.
However, in the Classic McEliece proposal (based on Niederreiter in spite of its name), they don't do any of that. They are giving lots of details as to why the two other modifications by Niederreiter (msg is the error instead of codeword, transmitting the Generator matrix in systematic form) don't reduce security, but they don't detail why the can just remove this scrambling. Why can they? (Can they?)