One of my pet peeves as a Puma QHI when TANS came into use was the pilots who tried to plan a diversion using the black box, rather than getting out a chart. The old HC1 was always short of fuel (sometimes even before takeoff). Quite often it's not possible to go in a straight line and features such as Salisbury Plain Danger area get in the way, requiring a lengthy diversion and far more precise fuel planning. Using a chart makes that issue immediately obvious, one glimpse is worth more than any number of key strokes.
One RAF Puma later ran completely out of fuel in Portugal and was damaged during the subsequent engine off landing. Not sure how much the pilot relied on GPS/TANS but his in-flight fuel planning was rubbish (and so was his crew co-operation as his crewman/navigator got to the point of threatening to hit him with the fire axe if he didn't land before the engines stopped).
But I can also think of a fatal accident where, if the pilot had made better use of the GPS, all on board might have survived.