Waterproof fabrics are only waterproof to a point – this does vary, and the more breathable ones are less waterproof. It’s expressed as a number like 15000 or 28000 but I forget what the number actually means.
mm H2O, i.e. you could put a 15m column of water on it and it wouldn’t leak (but the fabric would probably rip).
Breathable fabrics are usualy 3 or 2.5 layer laminates, the inner one is usualy a wicking mesh (0.5 is IIRC the cheap way of doing it by flocking the inner surface), the middle layer is a PTFE membrane which does the ‘breathing’, and the outer is the actual fabric. The fabric needs to be water repellant to stop it wetting and forming a continuous layer at which point the jacket will stop breathing (and any collected water will find it’s way in eventualy).
Maybe the straps were dry because that was the only bit that was dry on the outside and the straps are breathable enough that the jacket could still work?