I agree that it's usually not about how you really are. You're not supposed to answer in great detail how your life has been since the last time you met the person asking the question. That's why I said a common response would be "fine". However, you're wrong in saying that it's the same as "how do you do". It is absolutely not! You say "how do you do" once, and only once you meet a person for the first time. But it's going out of fashion to use that expression at all, according to my former (British native) English teacher.

As to whether or not to reply with "how are you", I'm not sure about that, but you're probably right that it would be impolite not to do it.