Ah, so the system sees a "lo" where there should be a "hi", hence "short circuit to minus", though "line interruption" might imply a momentary "open" dropping line voltage to zero. But, an open would not blow a fuse, so it should be assumed a short to GRD or high current draw.
Here is an interesting video -
Sheds a little insight. it appears that PTC heater and A/C are fed from the same fuse. They did not find a short either, despite the blown fuse! And several comments suggest that they have a similar issue with a 530e.
Does your heat work? Was the fuse replaced? It looks like the wire to A/C can be disconnected for testing purposes. Maybe the PTC heater too? Maybe the heater can be disconnected and the A/C left connected for troubleshooting? Have they tested the PTC heater system for excessive current draw? Including cabling?
I am also wondering if there are other fuses downstream, specifically for the heater, that might be removed for testing/current monitoring purposes. Or just one big honking fuse, located in a hard to reach area, for both A/C and heat and associated cabling?
On edit, it occurs to me that if this is the only fuse blowing, why would they suspect anything but the heater and A/C?