I can see the comparison, the mismatch of how the brain perceives the body and the actual physical body causing mental distress much like how the immune system reacts to a foreign body. Both sometimes result in physical harm to unwanted parts (BIID sometimes try to self-amputate, some with gender dysphoria try to cause genital harm).
I don't like using the word "normal" but neither one is a typical thing because obviously it would be much easier for the body and brain to match up but I guess the big difference between BIID and trans as people said it's much easier to live in a body that is corrected to match your gender than it is without a leg. But I'm sure those with BIID are much happier mentally once they loose that part of their body just like we are happier when we transition.