This paper investigates the combination of intensity-based distance maps with boundary loss for point-supervised semantic segmentation. By design, the boundary loss imposes a stronger penalty on the errors the farther away from the object boundary they occur. Hence it is inappropriate for cases of weak supervision where the ground truth label is much smaller than the actual object and a certain amount of false positives (w.r.t. the weak ground truth) is actually desirable. Using intensity-aware distances instead may alleviate this drawback, allowing for a certain amount of false positives with similar intensities without a significant increase to the training loss. This formulation is potentially more attractive than existing CRF-based regularizers, due to its simplicity and computational efficiency. We perform experiments on two multi-class datasets; ACDC (heart segmentation) and POEM (whole-body abdominal organ segmentation). Results are encouraging and show that this supervision strategy has great potential. On ACDC it outperforms the CRF-loss based approach, and on POEM data it performs on par with it. The code is made openly available.