I call the skill to address this issue "hearing intent." It requires listening beyond people's words. It inevitably involves intuition and relying on our instincts. This requires trusting our gut. Some ways to hear intent include asking ourselves the following questions: "Who is this person? What are they trying to say to me? Why are they saying that to me?"
Our response can then address what they were intending to say to us. True communication will happen. Time will be saved. They may seem a little bewildered at first. But they will ultimately appreciate it.
Like any skill this requires practice. Try it on for size when you are feeling bold.