I'm a therapist and you are incorrect.
One of the biggest problems with mental health is that people don't have stable "Love Objects" in their lives.
There's a whole form of psychotherapy called Object Relations Therapy about this topic.
To keep it brief, there was a famous monkey study where monkey babies were put in different cages with a mother figure. One cage had a mother monkey, the next a warm stuffed animal monkey, the next a statue monkey, the next a wire model of a monkey, the next a pole, and the final cage nothing but the baby monkies.
The babies with the best behavior were with the real monkey and their behavior declined as the female monkey became less realistic. The babies that grew up alone were very neurotic, nervous, and crazy.
Most mental health issues come from being raised poorly by your parents. That's because they were "unstable objects" in your life meaning you could not cling to them or they were missing. A psychologically distant mother is worse than having one made out of wire, for instance.
Animals, especially dogs, are some kind of amazing blessing in that they are massively affectionate and tend to be very stable. So, the human with a "comfort animal" is like one of those baby monkeys holding on to a "mommy" surrogate.
On an unkind note, people with mental problems tend to be very annoying. They are like the crazy lonely baby monkeys with nothing to hold on to. So, they are going to be annoying, attention seeking, and so on. That's why they need the comfort animal.