They have larger life threatening problems to deal with like earning their livelihood. There are always people around you and even if they can't help you they keep you distracted.
I've always wondered if that is the case. And if so, doesn't that mean there is a direct correlation between ease of living and depression? The less you have to worry about and deal with, the more likely you are to be depressed?
I suspect the most severely depressed in 3rd world countries, to be blunt, end up on the street and die (assuming they don't take their own lives first). That's one reason you may not see depression as obviously prevalent in the general population of a 3rd world country.
Humans were created to work, the harder they work the better they feel. Animals are the same way - if you give your pet an easy life, they will die early. Make them work (for example put their food where they can reach it, but have to work hard to get to it) and they live longer.
Developed countries have their own sets of problems. Developed countries tend to be more individualistic. In countries like India, you live a more social life, you can't just lock yourself up in a room and cry for hours. It is at least true for sub-urban area. You may like it or not there will be people around you. Life is also less automated. At many places you have to go and pay your electricity and phone bills. You will be more engaged most of the time.