Just because he or she is on medication doesn't mean he or she still struggles with depression. This person could be incredibly stable but still dependent on medication. Most people struggle with depression at some time in their lives or at least know someone who has depression. This leads to my next question...

If someone has struggled with depression in the past, is he or she immediately denied from working as a teacher in Korea? People can get over depression, just like any other health issue. Would it be possible for him or her to send a letter from his or her psychiatrist, explaining that he or she has recovered from depression? For example, several of my friends struggled with depression in high school due to certain situations, interpersonal issues, hormones, etc., but are now perfectly stable and well-adjusted adults.

However, that being said, if you're still struggling with depression, even with medication, I agree with the previous post, keep in mind that teaching in a foreign country can be very stressful. Discuss the choice with your doctor.

Also, isn't teaching privately on a tourist visa illegal? Seems risky...