Where you're coming from is a valid avenue, to me, considering that you're starting from a skepticism position and asking for some quality materials to review. I'm going to share some personal perspectives that might be relevant to your interest. As it's not peer-reviewed or an empirical study, but rather one based on 30+ years of experience, I do feel it's kind of in line with a personal psychology study. I don't get too specific out of personal reluctance.

For reference, I've got a physical handicap that is part of a spectrum. There are folks like me who can't go a couple weeks without medication, and others who have such a minor expression they would never know they had the condition unless in certain medical circumstances. In reality, some of those who would fit the diagnosis on a medical basis have lifestyles which would indicate they do not have the condition. On the flip side, my lifestyle has been forced to conform to the condition, so to speak, in order to appear "normal" on a day-to-day basis.

Because I received some special accommodations over the years, I got first-hand interactions with kids/youth with other conditions as well. When looking back at those years, I'm reminded of the (very real) condition labeled Obsessive Compulsive Disorder (OCD). Again, it's a disorder along a spectrum, not necessarily testable by blood, but there are methods for a diagnosis.

As the condition itself got more commonly known, the phrase "I'm a little OCD" started to seep into the US lexicon. In my experience, these were (most often) people who genuinely didn't have the condition who felt that by saying they had some symptoms, but, more than likely, would never fit the diagnosis. This was brought to my attention by a drummer friend in college, who genuinely had OCD tics (silverware arrangement before eating) and shared with me his frustration at the, well, minimizing of his condition.

The whole gist of this musing is that based on my upbringing, I've never wanted my condition / disability / handicap, nor would I want to be public about it and seek special treatment as a habit. As society in the US has changed to be more understanding and accepting of individual issues (to an extent), be it a handicap, socially progressive sexual preference and expression that used to be highly taboo, or a food-type allergy, I see there is a genuine trend towards special accommodations as a right to be fought for. It's a benefit to those who need it, but it's also an avenue for exploitation by those who feel compelled to do that...and when criticized, there's an immense push-back.

So, without being too glib, first it was OCD, then it was ADHD, and now it's Autism. Each one is genuine, and each has measurable symptoms with respect to functioning in daily life. However, unlike my condition, which nobody in their right mind would want or advertise unless for straight up bullshit sympathy, there are some benefits to over-stating one's personal affliction.

I've no doubt some people would take issue with this perspective, but if I'm framing it properly, that would potentially be the avenue for more research via psychology: Studying human behavior relating to adopting a negative for access to a positive. In the most extreme case, I'd reference when a person fakes cancer for sympathy and/or financial gain (of which there are documented cases), and compare that to parents who simply want to understand their child and will look all over for answers, or convince themselves that somehow what they've come across is the answer.