Stewrt is correct, you are should freeze transforms before reversing the normals.

You need to swap steps 3 and 4, you must freeze the transforms BEFORE you reverse the normals. It is the act of freezing the transforms that reverses the normals. You even get a warning message.

You can test it to see. Go to lighting and turn off 2-sided lighting. Then make something and duplicate and scale it -1. You will see the lighting does not change. Now freeze transform on the -1 scaled part. You will get a nastygram warning parts have become inverted and the -1 scaled part will turn black. Now its normals are truly inverted so now you can reverse the normals and finally delete the history.

the order should be

1. scale -1 to flip
2. freeze transforms (now the normals are inverted)
3. reverse the normals.
4. delete the history

You were flipping steps 2 and 3.