That sentence is misleading. Here's a better way to look at it:
Whether A problem is supervised or unsupervised depends on the nature of the problem you're trying to solve. In a supervised learning problem there's some ground truth you want the algorithm to predict. The ground truth could be a discrete label (Classification) or a value in continuous domain (Regression). On the other hand, an unsupervised learning problem doesn't try to "predict" some label or value. Rather, it tries to learn a better representation or structure of the data. Clustering and dimension reduction are both examples of unsupervised learning problems.
Now, in order for you to train a supervised learning algorithm, you do need to provide it the ground truth. Lack of labeled data does NOT make the problem unsupervised, it only means that you have to spend the effort to obtain the labeled data needed, or else you can't train your algorithm. In reality, it
is often unrealistic or too expensive to obtain labels/target value for all the data you have. Therefore, there is also a class of semi-supervised algorithms which does supervised learning using both labeled and unlabeled data, when certain assumptions apply.
In short, whether a problem is supervised or not depends on the nature of the problem. Some problem requires you to have labeled data in order to train your learning algorithm, and some do not, but having labeled data or not should NOT change the nature of the problem you're trying to solve.