Jetblu,
Checking the ident wouldn't have helped either. That was being transmitted on the LOC signal.
As SSD said, the crew had no way of knowing that the GS was unserviceable. The GS transmitter was left in a test mode which meant that only one part of the GS signal was being transmitted, which meant that an ON GLIDESLOPE would always be received by an aircraft, regardless of its location!
A further hole in the swiss cheese, was that due to construction, the tower was not able to monitor the ILS integrity.
So the moral here is to treat an ILS as unserviceable if it is NOTAMed NOT MONITORED.
From a design point of view, I am staggered that the equipment continues to transmit an ident, if the GS is not in normal operational mode.
Kudos to Air New Zealand for producing this video. I can't imagine corporate lawyers allowing that these days.