It is not possible to bypass the OIA. Any request for information held by an agency falls under the OIA whether the Act is mentioned or not.
As a result, the Ombudsman will now be reviewing the Ministry's OIA processes, and those across the wider public sector. I understand this practice of asking requesters to withdraw requests in order to get them processed is fairly common (though it has never happened to me), and hopefully this investigation will put an end to it.
Finally, the Ombudsman also expresses concern around the Ministry's attempts to manage information around the school closure process generally, and the widely-held perception by those affected that they are not being told enough. As a result, they will be investigating the Ministry's handling of such consultations, with a particular eye to how much information should be released proactively to inform people. Unfortunately, it looks like that won't be happening until the current round of sham-consultation is done and the decisions have been made public.