I'm wondering if he's being charged because he had the children with him and didn't tell anyone. I searched the Offenses Act linked in the Newsweek article and could only find this charge related to wasting Police resources.
"False allegation or report to Police
Every person is liable to imprisonment for a term not exceeding 3 months or a fine not exceeding $2,000 who,—
(a)
contrary to the fact and without a belief in the truth of the statement, makes or causes to be made to any Police employee any written or verbal statement alleging that an offence has been committed; or
(b)
with the intention of causing wasteful deployment, or of diverting deployment, of Police personnel or resources, or being reckless as to that result,—
(i)
makes a statement to any person that gives rise to serious apprehension for his own safety or the safety of any person or property, knowing that the statement is false; or
(ii)
behaves in a manner that is likely to give rise to such apprehension, knowing that such apprehension would be groundless."
I think the only thing that applies to his case here would be section b - being reckless causing the wasteful deployment of Police personnel or resources.
I could be totally wrong, this is JMO based on the article.
Edited with link to Act
Summary Offences Act 1981 No 113 (as at 01 August 2020), Public Act 24 False allegation or report to Police – New Zealand Legislation