"I assume that the corrections they are referring to are related to the chart vs the GPS horizontal datum. Is that correct?"
Now NAUTICAL LOG thought it was an excellent question, worth further research and comment, so from MARINE LINK here is what happened. During a coastal passage a containership ran aground after the Watchofficer (OOW) altered course about half a mile before he reached the intended alter course position. An investigation suggested that the OOW was reading GPS alone to plot positions and was not aware that a correction needed to be applied to the readings prior to plotting on the chart. The investigation suggested that a "more detailed passage plan would have alerted the inexperienced officer to the danger and required him to cross-check his position by more than one method". All NAUTICAL LOG can say is - possibly - however a properly trained OOW is taught to confirm the position by at least two methods. On a coastal passage a bearing and range is quick and accurate, the range can be from radar or a sextant angle - remember those - which leads to a whole other question of how many ships even have a sextant on board these days. Certainly one does not see officers carrying their own anymore and few ships, including passenger ships, have one supplied as part of the Bridge navigational equipment.
Anyway the investigation went on to say that seafarers must be aware that on many charts still in use a correction has to be applied to satellite-derived positions before that position is plotted on the chart. To comply with current regulations all this data should be entered up in the Passage Plan and OOW's be made aware of the corrections. So in answer to that comment which started all this - correct the charts and correct the GPS - correctly !!
GPS Error Correction
The Pennsylvania State University has done work on the causes of GPS error. The sources of error includes the clocks in satellites and receivers, the atmosphere, satellite orbits, and reflective surfaces near the receiver. The arrangement of the satellites in the sky can also increase 'dilution of precision'. Many of these errors are correctable within the equipment however navigators should be aware of a correction needed to correct readings prior to plotting.