The reason for the varied responses is that the question you ask is not only about the English language, but it also touches on etiquette, which is more idiomatic.
The short answer is: yes, the answer to "How do you do?" is "How do you do?" It is also acceptable to reply "I'm fine, and you?" and similar variations.
However -- and this is important to the etiquette side of things and not so much the language side -- "how do you do?" is actually not a question! It is a greeting, similar to "good morning" and, hence, an appropriate reply is also "good morning to you!"
Etiquette allows simple replies such as "I'm fine, how are you?" to appease the literalists who might feel off-put by a non-reply to what they mis-interpret as having asked you a question. However, good manners also prevents one from discussing their personal troubles with every acquaintance or stranger on the street who greets them with "good morning!" or "how do you do?" Hence, any reply in the form of an answer is always "I'm fine" (followed by "and you?", as a courtesy), and never "terrible! My stomach hurts and I have a splitting headache!"
Of course, if you are talking with a friend who truly inquires about your wellbeing, and you feel like sharing with them, by all means, do so. My answer is not meant to prevent that, only to allow you the dignity of a polite answer for passers-by that does not require you to spill your guts.