Deep learning models have achieved impressive performance in medical image segmentation, yet their black-box nature limits clinical adoption. In vascular applications, trustworthy segmentation should rely on both local image cues and global anatomical structures, such as vessel connectivity or branching. However, the extent to which models leverage such global context remains unclear. We present a novel explainability pipeline for 3D vessel segmentation, combining gradient-based attribution with graph-guided point selection and a blob-based analysis of Saliency maps. Using vascular graphs extracted from ground truth, we define anatomically meaningful points of interest (POIs) and assess the contribution of input voxels via Saliency maps. These are analyzed at both global and local scales using a custom blob detector. Applied to IRCAD and Bullitt datasets, our analysis shows that model decisions are dominated by highly localized attribution blobs centered near POIs. Attribution features show little correlation with vessel-level properties such as thickness, tubularity, or connectivity -- suggesting limited use of global anatomical reasoning. Our results underline the importance of structured explainability tools and highlight the current limitations of segmentation models in capturing global vascular context.