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 false positives the farther away from the object they occur. Hence it is intuitively inappropriate for weak supervision, where the ground truth label may be 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 without a significant increase to the training loss. The motivation for applying the boundary loss directly under weak supervision lies in its great success for fully supervised segmentation tasks, but also in not requiring extra priors or outside information that is usually required -- in some form -- with existing weakly supervised methods in the literature. This formulation also remains 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). Preliminary 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 for all our experiments is openly available.