We present a critical assessment of the role of transfer learning in training fully convolutional networks (FCNs) for medical image segmentation. We first show that although transfer learning reduces the training time on the target task, improvements in segmentation accuracy are highly task/data-dependent. Large improvements are observed only when the segmentation task is more challenging and the target training data is smaller. We shed light on these observations by investigating the impact of transfer learning on the evolution of model parameters and learned representations. We observe that convolutional filters change little during training and still look random at convergence. We further show that quite accurate FCNs can be built by freezing the encoder section of the network at random values and only training the decoder section. At least for medical image segmentation, this finding challenges the common belief that the encoder section needs to learn data/task-specific representations. We examine the evolution of FCN representations to gain a deeper insight into the effects of transfer learning on the training dynamics. Our analysis shows that although FCNs trained via transfer learning learn different representations than FCNs trained with random initialization, the variability among FCNs trained via transfer learning can be as high as that among FCNs trained with random initialization. Moreover, feature reuse is not restricted to the early encoder layers; rather, it can be more significant in deeper layers. These findings offer new insights and suggest alternative ways of training FCNs for medical image segmentation.