If someone says, "I don't need X" to me, I take it that they simply don't want it for one reason or another, hence why it's necessary to be careful with words.
People do not need to be more careful with their words, rather you need to be more careful with your understanding of those words. If someone says, "I don't need X", that means they don't need X. On the other hand, if they say, "I don't want X", then you can feel free to start arguing with them. Want and need are two different words with two different meanings.