Read this link carefully. Foreign investors can set up a trust in NZ, invest in a fund run from NZ that in turn invests only in foreign assets or financial instruments, but after JK's 'new tax rate', they'll pay no tax on that income. NZers who invested in the same fund, will have to pay tax at the PIE rate (28%). The extra advantage that hasn't changed I guess, is that foreign investors don't necessarily get their trust details bandied about, unless they are unlucky enough to be resident in a country we have a tax treaty with, and someone asks IRD in the correct way. No treaty, no details are passed on, full stop. In which case they'll probably not document their trust if they think they can get away with it, or they'll invest somewhere else.
When the tax rate was 28%, there would have been hardly any takers for these PIE funds. Then came the JK difference (NO TAX) and suddenly the money came flooding in. The settings were OK when Labour set it up, because the fair tax rate discouraged that type of investor. Maybe the trust rules need looking at too, but it's the combination of the trust rules and the new zero tax rate that constitutes a haven.
Since a trustee for a foreign trust has to produce a utilities bill and a passport to prove they are resident in NZ, but then only needs to state that the settlor is foreign based, with no further details provided, what is to stop a NZ fraudster from setting themselves up in a foreign trust here? The massive advantage is that they can then effectively invest in one of these foreign equity PIE funds, and pay no tax on the returns. As soon as the tax rate for one side is 28%, the other 0%, the obvious is going to happen.