The phrase thrid world country is a little outdated anyway. No one ever mentions second world countries for any reason. Most people probably couldn't even say what a second world country is, all they know is first world gets cable television and third world gets celebrities begging people to help.
While it is outdated, it is still used more than "developing nations". And true, most people would just be dumbfounded if asked about "second world" countries. Which, again, is condescending and another one that I wouldn't use.