Personal Opinion: Psychologists tend to be social people, who tend feel their way through life (that's why they want to study people); mathematicians are not social people, who tend to base their actions on cold logic (that's why they contemplate numbers); autistics are not social people (because they are ill). If we consider socialness (x) and illness (y) as two separate variables and plot them out, psychologists would be in the top-left, mathematicians in the top-right, and autistics in the bottom-right. Because psychologists have difficulty conceiving non-social personalities (being very social themselves), they kind of remove that variable when observing behaviour. This means that when they do personal observation, they tend to group autistics and mathematicians together on the right.
Summary: Psychologists have a huge inbuilt bias to overcome. I am not convinced that psychologists are easily able to distinguish between healthy analytic behaviour and autism.
Unfortunately, we have all seen incompetents in our own industry, It is unreasonable to assume that it does not exist in the psychology industry as well. In fact, the psychology industry has come under fire recently for lack of repeatable results: people just weren't testing one another's results.
I am a psychologist (I mean, I've got the degrees to be one, although I don't practice as such) and introverted. Yet I am a gifted psychologist, it can make a difference. I know several gifted psychologists and they happen to all be introverts too...
And, sometimes (oftentimes) giftedness is misdiagnosed as BPD, borderline personnality, and some gifted are wrongly seen as slightly autistic by others.
So, please, don't put us all into the same box; ;)
As I say, neither good nor bad, just a risk. Psychologists have chosen to deal with people, mathematicians have chosen not to. My observation is mearly a means of explaining some of the "misdiagnosed BPD, borderline, ...."
Interestingly, that a psychologist type personality took offense to my statement goes to my point... it is a statement of potential risk, I am assuming that "analytic personalities" would either accept it, or challenge the logic ... without being offended.