. . . In their case, a GPS receiver would have required a lot of batteries. Consider that they were out for 3 days plus they were lost for an additional 3 days, they may or may not have had enough batteries to last that long even if only using it for the hours they were hiking.
Again, only if you leave the GPS receiver on constantly. Turn it on, mark the position on both the GPS and on your paper map, turn the GPS off. 5 minutes out of the 9-18 hour battery life typical with a modern GPS. One set of batteries can go many days.
One fix with a GPS would have shown them they were nowhere near where they thought they were located.
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