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High number of writers, small number of training samples per writer with high intra-class variability and heavily imbalanced class distributions are among the challenges and difficulties of the offline Handwritten Signature Verification (HSV) problem. A good alternative to tackle these issues is to use a writer-independent (WI) framework. In WI systems, a single model is trained to perform signature verification for all writers from a dissimilarity space generated by the dichotomy transformation. Among the advantages of this framework is its scalability to deal with some of these challenges and its ease in managing new writers, and hence of being used in a transfer learning context. In this work, we present a white-box analysis of this approach highlighting how it handles the challenges, the dynamic selection of references through fusion function, and its application for transfer learning. All the analyses are carried out at the instance level using the instance hardness (IH) measure. The experimental results show that, using the IH analysis, we were able to characterize "good" and "bad" quality skilled forgeries as well as the frontier region between positive and negative samples. This enables futures investigations on methods for improving discrimination between genuine signatures and skilled forgeries by considering these characterizations.