Yes, I understand the concept that you quoted. Theoretically, it's more sound.

However, I want to point out that the purpose of the 'magic mirror' method is to ease mental math. It frees your brain from having to spend time / space on the extra step of applying the same operation to both sides.

Putting this in the context of 'showing your work':

Normal: x / 3 = 4 => 3 * x / 3 = 4 * 3 => x = 12

Mirror: x / 3 = 4 => x = 4 * 3 = 12

It's a bit complex to describe - I feel how you do basic math such as this is hardwired into your brain at a very young age.