How can anyone describe Raw Data as a "dire emergency"?
Nothing to do with raw data. They had the wrong heading displayed on both ND & PFD due to incorrect magnetic variation being applied, so they were unknowingly flying the wrong way even when they tried to follow ATC instructions. That could have been disastrous.
But why were they entering coordinates in the first place, rather than airport designators and waypoints?
We're talking about two different things here. Airport designators & waypoints are entered into the flight plan in the FMGS. The crew did this part correctly. The coordinates are needed to update the IRS and require greater precision. The crew did this part incorrectly.