The independence of the judiciary from politics means Mr Finlayson is unable to comment on specific cases.
Mr Matenga's refusal of the inquest - made public last Friday - also came with a broader order suppressing all details relating to the corporal's death including the Defence Force court of inquiry report.
The Defence Force has now refused to comment on any of the details of the case, saying Mr Matenga's suppression order means it is bound to silence.
Mr Matenga is a former bishop of the Church of Jesus Christ of Latter-day Saints and a recently appointed president of the cluster of congregations led from Temple View in Hamilton.
In November, he put forward a submission to Parliament which opposed Labour MP Louisa Wall's private member's bill allowing gay marriage.
"Changing the law to allow same-sex couples to marry is completely unnecessary and would serve no useful purpose," he said.
"A man and a woman are required to produce children. To allow same-sex couples to marry is a social experiment. There is no evidence to suggest that children will not be affected by it."
The Chief Coroner, Judge Neil MacLean, was unavailable for comment.