This is not entirely true.
As a guy with pretty bad BDD, I've been obsessed with this phenomenon for a while, and I've done some digging around. The flipped image of what we see in the true mirror might be what others see: it's not what others perceive.
We always look at ourselves in the mirror, so our brain has grown accustomed to the mirrored version of our face. Human faces are never perfectly symmetrical, but our brain filters these 'imperfections' out and tries to find symmetry. This doesn't just apply to our own appearance, but to the way in which we perceive the appearance of others as well. When we look at a flipped reflection in a true mirror, our brain sees something that it is not used to seeing. Even though we know it is our own reflection, it doesn't add up with what we remember. Therefore our brain will highlight the asymmetries or imperfections that neither we ourselves nor others would normally perceive. This is a psychological phenomenon called the 'Mere exposure effect', and has been researched numerous times in the past. This also explains why the majority of people dislike the way they look in pictures or on video. A simple way to confirm this is by having someone you're familiar with stand next to you in front of a mirror and look at their reflection. They will not look the same as you're used to, guaranteed.
In summary: I think the image that we see in a normal mirror is more accurate to the way others perceive us than what we see in a true mirror.
"If the world didn't suck, we'd all fall off."