Mental health problems exist on wide spectrum of different types of from things like schizophrenia or bipolar or borderline personality disorder through to eating disorder, anxiety disorders, OCD, or depression.
Some of these are very treatable.
People with a mental health problem should be able to seek help from that problem without being inappropriately sent to hospital for an asessment.
In this example the professional could have checked OP's understanding of the question. Modern guidance is to avoid questions like "do you intend to hurt yourself" and ask more direct questions such as "do you self harm?" and "do you have thoughts of suicide? Do you plan to kill yourself?"
A college counsellor is absolutely there to provide treatment and advice for the so-called "mild to moderate" end of mental illness.