Hi SAS, you are absolutely right. However, in the EC135 the caution lights associated with the Transfer pumps work in reverse. When the cavitate (they heat up) they show a warning. The attitude of the fuselage can cause this when the main contents reduce to a certain level. The standard practice seemingly being to select the offending pump OFF to extinguish the caution. In PLOD ops, a combination of balls out forward flight to get to the task followed by prolonged hovering, offers the two extreme conditions of nose down and nose up respectively, causing in the right (sic) conditions, both pump lights to illuminate sequentially according to attitude.
Poor airmanship can cause the pilots to forget to switch them back on again. Without a CVR or FDR we can never know for certain how this transpired in this accident case.
Like I said, we do know for a fact that fuel was not in the supply tanks. We know for a fact that when the aircraft was inspected by AAIB the transfer pumps were positioned OFF. One prime pump (in the supply tank) was positioned ON. We can only assume the role Dave played in these switch selections including how the switches ended up in the positions they were.
To imagine how the fuel starvation eventually took place, you are right, we have to imagine that despite the general low fuel state, the multiple warnings the CAD NVM implies he received...and acknowledged (by a switch on the cyclic), he seemingly never checked if the transfers pumps were working. To then take it to the unfortunate conclusion of double flameout and poor auto leading to zero NR at approximately 400 feet, it takes a huge effort to imagine this all occurred in sequence without Dave ever once taking appropriate action.
The contents indication theory is just that. A theory. Its only merit is that it offers us an opportunity to maybe understand to some degree why Dave did not react to the sequence that unfolded. Was what he saw on the gauges different to what the Cautions an Warnings he received telling him? Its just one possible explanation as why his implied actions were at odds with what was happening.