Health and Safety and scene preservation have nothing to do with the recovery of victims. Sometimes the risks are too great to proceed without specialist equipment or shoring, which takes time to arrange. Just diving in will end up with more casualties among the rescuers as debris shifts and collapses and will almost certainly hasten the demise of any victim(s).
The fuel sensor issues and possible misleading display of fuel levels are to some extent a red herring. Fuel gauges in all aircraft are notoriously trouble prone and are only an indication that some fuel is probably in the tanks. I was taught to manually dip the tanks to check fuel levels before every flight and calculate maximum endurance accordingly and subtract 30 minutes. That was the point I should be back on the ground, no matter what.
Even if the fuel had been in the supply tanks and not the main tank, the helicopter would have landed back at base well below the mandated minimum fuel load. What excuse would have been used to explain that? What sanctions would have been taken against the pilot, if any? Could the severity of any penalties for breaching minimum landing fuel have been preying on the pilot's mind? That would certainly be a distraction especially with doubts already being raised about fuel gauge accuracy in the EC135.
Maybe accepting the last tasking was simply resignation that the helicopter was below minimum fuel anyway, and it was only a couple of miles back to base. Might as well get hung for a sheep as a lamb.