As someone who go out of my way to recycle, I abhor companies trying to disguise cost cutting through a front of an environmentally friendly practice (don't know enough about Air NZ to say whether they are doing this but there are lots of companies guilty of doing this). But it's especially hypocritical when airlines start flaunting their environmental conscience when flying in an aircraft produces 90kg of CO2 per hour per passenger while a single water bottle has a carbon footprint of 82g. That's about 1,100 plastic bottles per hour in which one hour is the carbon equivalent of more than an entire year's consumption of bottled water for most people (and entire flight may be the equivalent of other people's entire carbon footprint in a year).

But back to OP's point, it is possible to actually re-wash and re-use plastic cutlery. Qantas did it. But that requires more analysis to calculate the carbon costs of operating the dishwasher, environmental impact of water, transportation, sorting, etc.