Let me guess? This must be a for-profit trade school.
Anyhow, what they're doing is legal. It might not be ethical or transparently honest, but it is still legal. They know that so many people still want to jump on the 'nursing' bandwagon, so they're simply catering to the masses by including 'nursing' in the title of the training program.
I would hope the prospective students do some research on what a psych tech really is, as well as their typical job duties, description, employment outlook, pay, and so on.
CNA programs are not training licensed nurses, but 'nursing' is still legally in the title. It's the same situation with the psych tech program, which is not a protected title by law.
BTW, I once worked at a psychiatric facility where the staffing coordinator's official job title was "nursing coordinator," even though she was not a licensed nurse at all.