BIID and BDD - two different conditions
It appears many people compare Body Integrity Identity Disorder (BIID) to Body Dysmorphic Disorder (BDD). The conditions are similar only at first glance and in fact quite different. There is more similarity between BIID and Gender Identity Disorder (GID) than with BDD.
Typically, individuals dealing with BDD have a distorted perception of their body. They think it is abnormal and seek to make it appear normal. For example, someone who has anorexia thinks they are overweight, and will seek to lose more and more weight (this is admitedly a gross simplification).
In contrast, transabled individuals do not believe their bodies are abnormal. We well know that our full complement of working limbs are completely normal. However, we are facing a deep ill-ease with these working limbs.
While it is possible to train individuals with BDD to change their perception (and even that's not a given, think of all the people who have BDD that end up killing themselves), it is not so simple to change the psyche of the individual with BIID. Just like transsexuals are not usualy "cured" by psychotherapy.