He said the "perception" of independence was as important as reality.
"Our most trusted news outlets cannot be seen as anything other than totally independent," Power said.
"It must be robust enough for different governments over time," he said.
Power said structuring the new organisation as an autonomous Crown entity gave RNZ and TVNZ less independence than their current existence as Crown entity companies.
"We do not believe a case has been made for reducing their independence," Power said.
"An autonomous Crown entity allows for ministerial direction, a Crown entity company does not allow for ministerial direction," he said.
RNZ board member Jane Wrightson and chief executive Paul Thompson agreed editorial independence in the bill needed to be strengthened.
Wrightson said the model demanded "absolute clarity about the overriding importance and priority" of the entity's public media goals, particularly with regard to its revenue-gathering role.
Wrightson noted that commercial revenue was a part of public broadcasters overseas, but the bill needed to be very clear that the entity's ability to "generate revenue… is only for the purpose of the entity to fund its public purpose and to carry out that objective in line with the charter".
Wrightson also suggested that the entity be given five-year funding agreements to prevent any government using Crown funding negotiations with the government to compromise its independence.
Two private media companies warned the proposed model could cause them to retreat from the market by making it more difficult to fund public interest journalism through advertising and by making that journalism more expensive.
This is because the media entity would be subsidised by taxpayer funding, whilst also operating commercially, but not having to return a profit.
This would give it an advantage when competing for staff and bidding for advertising. Commercial media companies are not largely taxpayer-funded, but have to operate commercially, while also making a profit.
Stuff chief executive Sinead Boucher said the public media entity was already being felt in the market already, with offers being made to Stuff staff.
"In some cases the salary offers have been 30 per cent above what we have been paying and what we are paying is very much the market rate - not low paying, so we are already starting to feel the effects of it and the entity is not even formed," she said.
Boucher is the owner of Stuff Ltd, a competitor to the NZ Herald's owner NZME.
Boucher said that public interest journalism was not only carried out by public companies - private companies also made public interest journalism.
"We are proud of our own role as a strong part of public service journalism in this country," Boucher said.
Stuff noted that the amount of te reo Māori content had increased on its platforms, while the amount of te reo Māori content on publicly owned RNZ had decreased.
Boucher said the new entity was a "chilling prospect".
"It is hard to see a situation where this entity would not be contributing to the well-publicised obstacles that the media has experienced," Boucher said.
Boucher said private media was facing a "pincer movement" from the entity, which could use public funding to undercut private competitors when it came to competing for advertising revenue and overpay when it came to competing for staff.
"We are already starting to see evidence of this in the way our staff are being approached and poached and offered salaries that are well beyond the market... in anticipation of this entity being formed," she said.
Glen Kyne, senior vice president and head of networks at Warner Brothers-Discovery, the owner of Three also warned that the new entity would have "market-distorting funding arrangements".
He said this would flow through into the production sector, which makes much of the content that TV and radio stations broadcast.
Kyne warned it could undermine "competition and innovation in the production sector".
He suggested that a portion of the media entity's surpluses be "reinvested in a contestable fund that it can't access".
Other media companies, including Mediaworks and NZME, the owner of the NZ Herald, will submit on the bill in the afternoon.