I think he was just trying to save a Quaternion creation. Your way does more work and may not produce the right answer anyway. (at some point a quaternion’s rotation might spill over into the angle you aren’t inverting in a way that randomly causes issues.)
It’s not really mirroring… it’s just applying the rotations in the wrong order which in some cases may appear to be mirroring.
This effect is easy to see. Let’s say you have a rotation (A) about the x axis of 90 degrees and a rotation (B) about the y axis of 90 degrees. Apply these to your head. ie: A is nodding yes, B is shaking your head no.
First B then A. You will be looking up at the ceiling with your chin over your shoulder.
If A then B you will be looking at the wall over your shoulder with your ear on your shoulder.
Remember, rotations are relative to the current reference frame.
…and I wouldn’t call either of those a mirror image of the other.