I would find that difficult to believe. Twin engine helicopters don't usually do fuel exhaustion simultaneously on both engines. Normally one engine will run out of fuel a few minutes before the other one. In which case, when the first engine went quiet a radio call would go out pronto. Not-withstanding a radio call should have already gone out when it was realized the required fuel to destination was more than the actual fuel on-board. There was no such radio call in this instance, as far as we know.
And if you really screw up your fuel planning and don't have enough fuel to get to your destination, and you're over hostile terrain, I should think the M/E pilot would choose to shut down one engine and leave all the fuel for the other engine to maximize range and get you as close as possible to a suitable landing site.