So when the US hires someone to do grunt work for them then it's not an US operation anymore?
Are you claiming that the US led the assault and had full operational command? Are you claiming that the US made the decision for the NZ government? Are you claiming that money changed hands somewhere?
Do you have proof of anything beyond, "This is a shocking turn of events, and I don't like it?"
Here are a number of other posibilities:
1. The NZ authorities don't have a lot of experience with assaulting a multi-million dollar compound to make an arrest.
2. The NZ authorities saw this as an excuse to perform a paramilitary operation.
3. The NZ authorities saw this as an excuse to justify the budget for their 'toys.'
4. The NZ government did this favor expecting to be able to ask the US for a favor later.
...etc...
If NZ wanted an excuse to walk their toys then there's never a shortage of drug dealers and other obvious targets with better publicity.
Why would they go ballistic over bagging an overweight computer-fraudster?
There is no plausible explanation other than somebody demanding special effects.