Outwood Grange Academies Trust has refused to say how much money it has spent on "political and media relations firm" Abzed which it initially used to field questions about "flattening the grass".
The multi-academy trust said disclosing how much money it had spent on Abzed "would prejudice our commercial interests".
However, one union leader urged the academy chain to be transparent about how it spends taxpayers' money.
How the story broke: Outwood Grange uses crisis managers to explain ‘flattening the grass’
Investigation: Insiders allege Outwood Grange ‘ritually humiliated’ pupils
Read: Teaching at 'flattening the grass' school 'felt like being a prison warden’
Last month, Tes asked Outwood to explain a policy know as "flattening the grass".
The trust did not provide an explanation, but several weeks later Tes published multiple accounts from trust insiders.
They alleged that the practice involved rolling assemblies at newly taken over schools, which were flooded with Outwood executives who engaged in the “ritual humiliation” of pupils to “terrify” them into compliance. Outwood Grange later challenged these accounts.
When Tes first went to Outwood, its response was coordinated by Abzed.
The response Tes was given failed to address what "flattening the grass" meant, and Abzed also suggested there was no connection between rolling assemblies and flattening the grass – something contradicted by eyewitness accounts Tes later received.
On its website, Abzed says: “Our clients arrive with a crisis. They stay because of exceptional delivery". In addition to Outwood, its clients include the fracking firm Cuadrilla, grouse moors and the e-cigarette industry.
Tes submitted a freedom of information request to Outwood, asking how long it had used the services of Abzed, and how much it had paid the firm.
In its response to the FOI, Outwood said that the trust "began working with Abzed from 1 January 2019 to date". However, Outwood declined to reveal how much it had spent on their services.
"OGAT believe that the disclosure of contractual information with this supplier would prejudice our commercial interests," the response said.
"The disclosure of this information would be likely to compromise our and our supplier's commercial position and future procurement exercises.
"While there may be public interest in this information, it should be noted that the trust is subject to regular scrutiny by bodies, such as the Education and Skills Funding Agency, external and internal audit to ensure it spends public funding prudently.
Outwood said that following a "public interest test", it had therefore decided not to release this information, citing the "commercial interests" section of the FOI Act.
Mary Bousted, joint general secretary of the NEU, said that while MATs might sometimes need media relations advice, Outwood should reveal how much it had spent on the firm.
“The money that Outwood Grange is being given, I don’t think anybody thought that this would be money used to pay for public relations companies to deal with adverse publicity," she said.
"If the fact is that that’s what they’re doing, then yes, I do think they should be making that public.
"If they’re spending that money on public relations companies…then they’re not spending that money on teachers’ salaries or on textbooks or on photocopying.”