True, believers can quote his actual words. However, whether those words are quoted in context or with the meaning Jesus intended when he uttered them is another issue. For instance, have you ever noticed how often Jesus' opinions on the various societal issues of our day always seem to match those making the argument? Really, it's absolutely uncanny (note sarcasm). Whatever the issue is and whatever side of the aisle the argument comes, there Jesus stands as well.
I want to be clear that Jesus might have plenty to say on some of today's most pressing concerns. In many cases, he does give us guidance through His example, through His teachings, and through His Spirit. However, all who claim to follow Jesus must appropriate all "Jesus leading" with great humility and recognition of the possible encroachment of our own biases onto what we think Jesus would do about 21st Century issues. We can speak on His behalf. In fact, we are often called to. However, when we presume to do so, we must do so with utmost care.
At this point in time, we run the risk of fatiguing the world of Jesus talk. Frankly, I wonder if we run the risk of fatiguing Jesus of Jesus talk. Perhaps we would do better to simply say what we ourselves think. We are those who are led by His Spirit and committed to following Him. So, our opinions ought to resemble His at some level. But, they may not always be the same.
Jesus needs to have a voice in today's world. However, if it's really His, it will be a different voice than mine occasionally. If it's really His, it will also always be a better voice than mine.