This appears to be the case, given the 'XKEYSCORE' program referenced. As current information has it, XKEYSCORE is not a collection program so much as system for storing and searching against the nearly unimaginable reams of data that is collected by other programs.
In other words, it is a gigantic searchable database of all the data that has been collected by the Five-Eyes agencies.
So, what NZ did was to submit a search to this database through the XKEYSCORE system, the format of which is as published in the linked PDF.
Some of that vast cache of data would have been gather by the GCSB as part of their participation in this unholy alliance but it might not have been this particular data and even if so, that interception was unlikely to have been targeted for this purpose. More that what has already been collected was searched for this rather non-critical, non-National Security purpose.
Which is why blanket collection and storage is so fucking heinous; it can be used for nearly any purpose. And this is exactly why the meta-data scheme doing the rounds in Australia is equally bad - it's a big, long-lived record that, while it 'justified' base on something, something, National Security, once it is there, no protections exist to prevent its use for other purposes.