Why does protein folding not depend on the order in which it is synthesized?
I suspect the author meant something a little different. It's not just that it doesn't matter if a protein is synthesized from N- or C-terminus it's also not important for the end result of folding that the synthesis is gradual at all.

When designing proteins de novo they model the folding on a computer. The gradual addition of amino acid residues to the protein is not part of these models, the computations are made on the entire sequence at once. Still, when the designed proteins are synthesized on ribosomes they fold correctly. So the fact that the proteins are built step by step shouldn't influence how they are folded very much. As long as there is a sufficiently low free energy state it will be achieved.

Also, N-ser-gly-ala-glu-pro-asp-C and N-asp-pro-glu-ala-gly-ser-C are not exactly the mirrored images of each other. They just have terminal amino and carboxyl groups swapped. I imagine this can influence folding a bit.