The importance of parameter selection in supervised learning is well known. However, due to the many parameter combinations, an incomplete or an insufficient procedure is often applied. This situation may cause misleading or confusing conclusions. In this opinion paper, through an intriguing example we point out that the seriousness goes beyond what is generally recognized. In the topic of multilabel classification for medical code prediction, one influential paper conducted a proper parameter selection on a set, but when moving to a subset of frequently occurring labels, the authors used the same parameters without a separate tuning. The set of frequent labels became a popular benchmark in subsequent studies, which kept pushing the state of the art. However, we discovered that most of the results in these studies cannot surpass the approach in the original paper if a parameter tuning had been conducted at the time. Thus it is unclear how much progress the subsequent developments have actually brought. The lesson clearly indicates that without enough attention on parameter selection, the research progress in our field can be uncertain or even illusive.