No, psychology is right. Psychology studies what the properties of thought are. Neuroscience studies the specific biochemical mechanisms of the brain. Psychology is the study of what mental reasoning IS, while neuroscience is the study of HOW neurons in our brain implement it.

If you are asking “ok, but what is reasoning, really? What definition of reasoning would enable us to recognize whether it is going on in this AI or not?” it is a question of psychology. Unless we are restricting ourselves to whole brain emulation only.

Psychology is stuck in pre-Galilean era. Even if it studies "properties of thought", as you put it, it does so without formal basis, let alone understanding from first principles. As Chomsky said, about psychology and the like, "You want to move from behavioral science to authentic science." [1]

[1] Chomsky & Krauss (2015) An Origins Project Dialogue at https://youtu.be/Ml1G919Bts0