These are the British & Irish Lions and nothing less, yet even that is not the whole story.
Warren Gatland, the coach, is one of the New Zealanders dominating the modern game. He may have spent most of his coaching years in the northern hemisphere, but he retains a house in Hamilton and an ambition to lead the All Blacks.
He is theirs, not ours. This is the British & Irish & New Zealand Lions, really.
Just as a World Cup victory for England in 2019 would be an Anglo-Australian achievement, due to the nationality of Eddie Jones.
We cannot pretend that those invited to do what British coaches, apparently, are unable to do have left their national influences and learnings at the door.
Jones' manner is straight from the southern hemisphere, and Gatland is only sent up as conservative or unimaginative, when compared to the freewheeling style in his homeland.
Wales have frequently played the most creative rugby in Six Nations matches and what his critics have mockingly dubbed "Warrenball" is hardly an unfamiliar sight in the north.
As he has proved on this tour, Gatland takes considerably more risks than the majority of his contemporaries. He is still Kiwi at heart.
At the time of the Rugby World Cup draw in Kyoto, six nations - New Zealand, Ireland, Wales, Japan, the United States and Georgia - were utilising Kiwi expertise, while Vern Cotter was technically still coach of Scotland, even though Gregor Townsend had named his first international squad two days earlier.
It is not just a rugby trait, either. If one looks at sports such as rowing and sailing, coaches are one of New Zealand's great exports.
According to Steve Tew, chief executive of the New Zealand Rugby Union, much of this is down to size. There simply aren't enough top coaching jobs to go around in this corner of the southern hemisphere, with just five Super Rugby franchises across New Zealand.
So talent drains.
Dave Rennie is a recent loss. He won three straight world titles with the New Zealand Under-20 team and two Super Rugby titles with the Hamilton-based Chiefs franchise, but has taken up a job with Glasgow Warriors for 2017.
New Zealand coaches in exile often have countrymen as assistants, too, such as Greg Feek, the scrum coach to Joe Schmidt with Ireland, and Tony Brown, who is departing for Japan with Jamie Joseph.
Tew says there is no plan to train up coaches abroad, although it is no secret that when Cotter applied for the All Blacks job previously, he was told to go away and get international experience.
A three-year spell with Scotland later, he is now biding his time at Montpellier, waiting to see if his application will be more favourably considered when the selection process for Steve Hansen's successor begins.
What this affords is an invaluable learning experience. Hansen has a 90 percent winning record as All Blacks coach, forged partly in Wales, where he won 10 tests in 30 and presided over a run of 11 straight defeats.
He is celebrated for making Wales fitter, more professional and better trained, but mystified some players with bizarre man-management techniques.
On one occasion, he allowed the players a night out during a training camp in Lanzarote, which some enjoyed to excess. The next day, he asked for those who did not make it to breakfast and those who had vomited in corridors on returning to put their hands up.
He then let them sit out a very hard fitness session. His explanation was that he wanted them to feel guilty watching their team-mates sweat.
They didn't. And the trainers felt like saps for behaving.
When Hansen returned to New Zealand, it was to work with Sir Graham Henry, who also benefited from positions with Wales and the Lions, and by the time he was made head coach, no doubt he had got any flawed psychological experiments out of his system.
Against this production line, where are England's coaches of the future?
Before Jones, the RFU's last two appointments could not have veered further from the exacting demands of the New Zealand model. Stuart Lancaster's career was largely in development, while Martin Johnson was a great player, forced to make his mistakes as coach at a World Cup.
England's options are a joke compared to those New Zealand enjoy.
Hansen says he will step down after the 2019 World Cup, at which point the board of New Zealand rugby will be able to call on a list of candidates, potentially in double figures. By comparison, what preparation is there for life after Jones?
What lessons learned from the chastening experience of having to look beyond England's borders?
The recently appointed coach of the New Zealand sevens team is Clark Laidlaw, who, although working there since 2008, was born in the Border region and is the cousin of Scotland captain Greig. Yet one gets the impression the All Blacks are sacred.
"There is no rule precluding a foreign coach, but I hope it wouldn't happen on my watch," Tew told me. "That would be disappointing. I'd hope we're producing enough coaches for the All Black job.
"It comes down to this - whoever enters the All Black environment has to be able to add to the history and legacy, to leave it better than it was. To do that you've really got to understand it, you've got to have a good feel for what is going on in New Zealand rugby at the time.
"That doesn't mean you couldn't give the role to someone coaching overseas, but they'd have to demonstrate they knew what the All Blacks require and what makes New Zealand rugby work. Our team is expected to perform well above the levels of any other.
"The New Zealanders coaching overseas, no-one would argue they are not still New Zealanders. But if any of those guys wanted to come back, they would have to prove they understood modern rugby and the talent we have available."
It's what you call a philosophy. It's also the difference between producers and consumers.
- Daily Mail
