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.