Interesting that there wasn't a "GS Check Height" on the chart (no outer marker due to the water under the approach). There is a LOC profile on the bottom of the plan view but was there a DME-GS check in the SOPs (granted the ILS DME was sus in this case)?
At one of our airports, the service provider wants to get rid of the markers. Cost too much. Replace them with DME-GS checks. Perhaps this is not a good idea. As happened to this crew, under high workload (falsely caused by the premature capture of the glideslope and subsequent stuffing down of the nose to follow the (false) glideslope), a crew could miss the GS check if it's based on DME. Done it myself. A marker beeping and flashing at you is much more likely to get your attention.
Congrats to this kiwi crew who were put in the ultimate gotcha situation, realised it and survived.