Article 19 of the income tax treaty in force between New Zealand and the United States sets out which country gets taxing rights to pensions from government service.
Not to be confused with social security benefits, which are only taxable in the source country (New Zealand in the case of superannuation, and United States in the case of Social Security) pensions derived from government services are taxable in the country to which the services were provided.
That is unless the individual is both a permanent resident of and a citizen of the other country.
For example, a pension paid by the United States from government services is taxable only in the United States. Unless the individual is a resident of, and citizen of New Zealand, but not a permanent resident or citizen of the United States, in which case a pension paid by the United States government (not Social Security) is taxable only in New Zealand (Article 19 Paragraph 2(a) & (b).
If the individual is a permanent resident or citizen of both New Zealand and the United States then both countries are able to tax the income.
This arises out of two provisions of the income tax treaty:
Article 19 2(b) provides for taxation of the country in which the individual is a permanent resident or citizen only.
Say this happens to be New Zealand. New Zealand would be the sole taxing country in the absence of the saving clause in Article 1.
Applying article 1 allows the U.S. to tax the pension as well should the individual be a U.S. citizen or a permanent resident (green card holder).
The U.S. Model Technical Explanation clearly indicates this on page 60:
However, an individual who receives a pension paid by the Government of the other Contracting State (United States) in respect of services rendered to that Government shall be taxable on this pension only in the other Contracting State unless the individual is a U.S. citizen or acquires a green card.
Article 22 of the New Zealand/United States tax treaty Relief from Double Taxation is not affected by the Saving Clause, and accordingly a U.S. citizen or resident should be able to re-source income in the U.S. tax return and claim a credit for New Zealand income tax paid.