To quote myself:

The stigmatization and punishment comes from people mostly outside the medical field and is a real problem well worth discussing,...

You said it yourself, it's a social stigma. It's a problem that won't be solved by not diagnosing, but by educating the ignorant people keeping that stigma alive.

If a condition is caused by the psyche it is, by definition, a mental disorder, or at least a symptom of one, and you don't need to be an expert on the field to know that.

What I can agree on, is that maybe obesity on it's own should not be thought of as a mental disorder, just like being underweight isn't. Often a lot of the underlying reasons for it, or denial of it, however, are. Just like all underweight people aren't anorexic. From what I know, most of obesity treatment acknowledges this, so you do have a point, though.