I think you're really missing the point. Of course, in an ideal world issues that are solely medical would be treated only as so, but a humanistic and holistic approach would be taken for every other issue a person has, having anything to do with any aspect of their character, choices, and life experiences. People get this. Thinking of someone as a "whole person" and not just labeling them as a disease is optimal.
However, this is a person trying to gain admission to a medical school, and if there is any reason for an admissions officer to reject them and choose someone else they most likely will. For people who know about and who have experience working with people affected by personality disorders (every clinician), this may strike an internal chord and cause them to immediately say no. Personality disorders are highly stigmatized (though avoidant maybe the least), and while they can be helped sometimes, they generally cause major problems for those who have them and most people around them. The fact that the poster has insight and is even aware that their personality is the problem in their life and has been willing to work at this problem most likely means their case is not 100% terrible and can possibly be treated and managed to an extent with a lot of help. However, it is STILL probably not wise to attempt to spin this in an interview and make some sort of strength out of it, even if it may be true. This is a highly competitive process and you should do everything possible to help your chances, which means not disclosing optional things that may end up hurting you. Admissions officers most likely do not want to hear anything about personality disorders.