I agree that the answer to your broad question is that "it depends". However, an example of a justified interview might be for the school psychologist to interview a student referred to him by a school professional on the belief that the student might need interventions for some perceived disability or deficiency. The school has an affirmative duty under the law to find any child that might need such services. If the school psychologist thought the referral justified a more formal evaluation, then the school would have to get the parent's permission to do such an evaluation.
As Mr. Corchnoy stated, public schools have an affirmative duty under "Child Find" which is part of the IDEA (Individuals with Disabilities Education Act) to identify, locate, and evaluate all children with suspected disabilities.
Have you attempted to contact the school psychologist? I would do so by email - be courteous, non-accusatory and state your concerns.
In this scenario, it really depends upon what the conversation was about and what was the school psychologist's purpose for the conversation. Often times children are questioned without a parent's knowledge or consent for issues such as bullying situations simply as a witness, or a school staff or faculty member may have a concern about a child for one reason or another, or perhaps the school had a concern and part of the duty of a school is to "find" children who may require additional services related to special education. There are many factors that can be considered. However, if you have a concern, email or call the school psychologist and simply state your concern and ask what the questions were regarding. If the issue was concerning something serious, then perhaps ask why you were not notified and why your consent was not requested. For the future, perhaps find out in what situations the school psychologist must have a parent's consent or knowledge before questioning a minor child.
By answering this question, this does not create any attorney client relationship between the parties and this answer is meant for educational purposes only.