Indeed, you may be perfectly correct.
He had the fuel on board, and must have known how low the main tanks were getting. One wonders why he didn't use the aux tanks, or if he did (that seems a possibility in the report) why he didn't use them earlier and therefore for longer? he seems a switched-on sort of guy who would be aware of what was going on.
Logically of course he wouldn't save fuel by not using the aux tanks for longer, simply increase the risk of the mains running dry. Yet the report makes quite a point of his keenness to save fuel costs wherever he could, and the accident was the result of fuel starvation, even though he had it on board but in the wrong tanks. There may be absolutely no connection there, of course. Or there may have been some sort of subconscious reluctance to use what was in the aux tanks.