This reluctance on Turnbull's part to take an inclusive approach towards New Zealand is where the Anzac sloganeering falls down.
Businesses on both sides of the Tasman are enjoying the fruits of work done through the single economic market process to make transtasman business more efficient. This was clear at the recent Australia NZ Leadership Forum in Sydney.
But the Anzac concept is substantially grounded on New Zealand and Australia "joining forces to take on global threats".
Turnbull is hosting some big names at the Asean-Australia Special Summit. Leaders of nine of the 10 southeast Asian nations that comprise Asean are present in Sydney. Philippines President Rodrigo Duterte decided not to attend.
Big issues are on the table, including China's assertiveness in the South China Sea and North Korea's nuclear missile programme.
But what looms as the biggest threat is a trade war.
The leaders are under pressure to present a united front in the face of the rising threat to free trade.
Already, Singapore's Lee Hsien Loong has said that all countries, big or small, will suffer if "tit-for-tat" trade wars break out.
To be fair to Turnbull, New Zealand was not on his dance card either when he hosted the first Asean-Australia special summit in Vientiane in late 2016. But this time he is on home turf. And the atmospherics have changed. The world is in a darker place.
It's not hard to get the impression that if John Key was still Prime Minister, he would have found a way to wangle an invitation to take part in the Sydney summit. And that Turnbull — who, after all, ensured Key was appointed an Honorary Companion to the Order of Australia (that country's highest honour) — would have humoured him.
Then there is precedent.
When Australia hosted the G20 Summit in 2014, Turnbull's predecessor, Tony Abbott, extended an invitation to Key to take part. Key played a strong leadership role in the trade discussion by G20 leaders (at Abbott's request) and made useful interventions in the discussions on the global financial system and some of the risks that lay ahead. These were acknowledged publicly by World Trade Organisation director-general Roberto Azevedo.
There is no doubt that Ardern, who is a quick study, could also have made a useful contribution. And that an invitation to Sydney would have provided her with the opportunity to clarify some mixed messages on where New Zealand stands — particularly on Russia and China — where her Foreign Minister has ruffled feathers through a lack of precision.
It would also have acted as an incentive for Ardern to continue to lift her game. After all, she has led a Government which — subject to relatively minor and somewhat cosmetic modifications — signed TPP-11.
A number of the Asean leaders are taking the opportunity to drop in while they are in the neighbourhood. Ardern hosted Nguyen Xuan Phuc — Prime Minister of Vietnam — earlier in the week. Indonesia's President Joko Widodo will arrive in New Zealand tomorrow for a two-day visit.
But the pivotal point is: Australia is looking outwards.
While New Zealand focuses on the incremental gains within the single economic market, Australia is focused on making major inroads in the region. The broader strategic game is for Australia to embed itself further with Asean, which in aggregate is its third biggest trading partner, partly as a hedge against an economic over-reliance on China.
A CEO forum is looking at topics vital to deepening economic integration, including gri-business supply chains, infrastructure, digital transformation, future energy, tourism and aviation. This will culminate in policy recommendations for the leaders at the Special Summit to bolster the ASEAN-Australian trade and investment relationship.
It's my view that New Zealand should have been included in this initiative. The failure to do so makes a mockery of the intent of the ANZAFTA and CER.