Being a New Zealander myself, albeit one who lurks more than posts, I guess I should chuck my 2 cents worth into this discussion.
I completely understand how the word "black" can be taken out of context, but in this instance this train of thought couldn't be further from the truth. Most NZ international sports teams wear a black uniform so the trend grew out of this. The first such instance was with the All Blacks, the national rugby team - there are a couple of trains of thought as to how this originated but I do believe that it was in 1905 when the New Zealand team was touring Great Britain. It is attributed to either a typo (the daily Mail newspaper talked about the NZ forwards (the big grunt guys up front) as having the skills of the smaller faster backs and described the team as "all backs" which was then possibly mistakenly written as all blacks) or in reference to another newspaper article which descirbed the team as all in Black except for the Silver Fern (the emblem on their jersey)on their chest and their bootlaces. However it came about it was something that came out of the English press.
However it eventuated, in the world of rugby you couldn't find a team which is more respected and ethnically diverse than the All Blacks. New Zealand is an extremely diverse country with a high European population along with the native Maori people, people from just about every Pacific Island, India, Asia and immigrants from Britain and South Africa. Over the years the All Blacks have been represented by people from almost all of these different and diverse groups.
The trend of calling our teams "black" grew from the All Blacks as other teams adopted a black uniform, one which because of the All Blacks was instantly recognisable as New Zealand (particularly amongst the Commonwealth and rugby playing nations of the world) Sadly it has gotten to the point of overuse, amongst others we have the Black Caps (cricket team) Black Sticks (womans field hockey team - also jokingly called the "Stick Chicks"

) and of course the Tall Blacks.
FYI the All Blacks are the number one ranked rugby team in the world and are the most famous and powerful brand in world rugby to the point where Adidas uses them as one of their banner teams for advertising globally - but obviously not in the US where rugby isn't a strongly followed sport.
So as I mentioned the word in this instance could be taken out of context but is not the case however it may seem, a quick look at some of the pictures of the All Blacks will quickly illustrate that there are some pretty big, mean guys who wouldn't take kindly to being in a team which was named in terms of race!