Firstly let's acknowledge that we are the only country in the world to call the rubberised sandal-like footwear so common on NZ beaches over summer, 'Jandals'. Other less refined souls call them flip-flops, or in Australia, thongs - presumably because they look like G-String pants for your feet. And there is a good reason for this - the word Jandal is actually a trademark, and for years was owned by Skellerup, a NZ company with a Danish name, before the manufacturing was moved to Malaysia and the brand was sold to Sandford Industries.
They've had to defend the trademark and the NZ High Court is considering whether 'Jandal' can actually be a trademark any more. As you can see, things are already looking shaky here. There is another reason that any claim that NZ 'invented' the footwear is tenuous - the Japanese have been wearing sandals with basically the same design for hundreds of years (the traditional woven-soled z_ri).
One of the 'inventors' of the NZ sandal even acknowledged that it was the sight of US businessman wearing rubber versions of the Japanese sandal that made them want to manufacture something similar in NZ.