McElrea, who is a chairman of the northern region of the National Party and chairman of Prime Minister John Key's Helensville electorate raised the issue with the board.
Concerns were picked up by chairman Neil Walter who said NZ On Air coveted its political neutrality. But the intervention by the NZ On Air board - which is seeking legal advice on extra powers to restrict timing for programmes - has been over the top and had the opposite effect.
It has raised questions about the degree the organisation is scared of offending politicians.
The appointment of McElrea - with has strong political connections - as gatekeeper for political documentaries is a surprising lapse from Walter, who is expected to resign early due to ill health.
Rather than abiding by political neutrality NZ On air has ignored a perceived conflict of interest over allocation of public money.
It is understood that Prime Minister John Key strongly supported McElrea's appointment to the funding committee in 2009. McElrea is a former executive at TVNZ but was not involved in documentary making or news.
As a member of New Zealand On Air he also has a say in the allocation to current affairs shows Q & A and The Nation. NZ on Air cut funding to The Nation last year - a decision that led to Sean Plunket losing his interviewer job.
Acting chairwoman of The Screen Directors Guild of New Zealand, Janette Howe said: "We have a lot of members putting pressure on us to ask Stephen McElrea to resign. His actions have shown poor judgment and there are real concerns that as he leads a documentary working group responsible for selecting titles within strands that he will bring his political hat to the table in this role.''