Estimating the uncertainty in (probabilistic) image registration enables, e.g., surgeons to assess the operative risk based on the trustworthiness of the registered image data. If surgeons receive inaccurately calculated registration uncertainty and misplace unwarranted confidence in the alignment solutions, severe consequences may result. For probabilistic image registration (PIR), the predominant way to quantify the registration uncertainty is using summary statistics of the distribution of transformation parameters. The majority of existing research focuses on trying out different summary statistics as well as means to exploit them. Distinctively, in this paper, we study two rarely examined topics: (1) whether those summary statistics of the transformation distribution most informatively represent the registration uncertainty; (2) Does utilizing the registration uncertainty always be beneficial. We show that there are two types of uncertainties: the transformation uncertainty, Ut, and label uncertainty Ul. The conventional way of using Ut to quantify Ul is inappropriate and can be misleading. By a real data experiment, we also share a potentially critical finding that making use of the registration uncertainty may not always be an improvement.