Dear Pandara,
With due respect, maybe you should consider changing your approach to students approaching you with depression. Clinical depression is a disease, just like cancer or diabetes. I can't imagine you telling a cancer patient that they suffer from an inflated ego.
Should your students come back for a second lesson, you will find that yoga and mindfulness can benefit them in many ways. This has been documented by such diverse authors as Amy Weintraub (Yoga for Depression - A compassionate guide to relieve suffering through yoga) and Marc Williams (The Mindful Way through depression).
If you would take a more compassionate approach, you would not deprive these potential students of the blessings of yoga.