Mr Joyce said Vodafone made its own decision not to participate after that discussion.
However, even after speaking to Mr Joyce two weeks ago, Vodafone has said its views are closely aligned with those of the coalition.
Vodafone's position was made clear in its submission on government proposals to override the commission's cuts to internet prices and was unlikely to have been changed by Mr Joyce, Ms Chetwin told the Herald yesterday.
"Companies like Vodafone are very well aware of the issues, they're right in the heart of it. An explanation by a senior Cabinet minister of what his view of the world is would not have persuaded them [either way]."
Ms Chetwin said it was something other than the strength of Mr Joyce's arguments that persuaded Vodafone not to join the coalition.
"It was political pressure presumably on other things that made them pull out."
Mr Cunliffe attacked Mr Key in Parliament yesterday over the proposal to overturn the Commerce Commission's recommendation.
He later described it as "corporate welfare" for monopoly network company Chorus that would see New Zealanders pay $150 a year more for internet than they should.
"National is once again propping up big business at the expense of Kiwi families."
Broadband prices
Why are people arguing over copper?
Despite the construction of the Government's new fibre optic Ultrafast Broadband (UFB) network, most New Zealanders still access the internet via old copper telephone wires.
How is the price set?
Because former Telecom division Chorus has a monopoly over the copper network, the prices it can charge are set by the Commerce Commission. It has recommended cutting the price Chorus charges its competitors and ultimately their customers by about a quarter, or $12.50 a month.
Cheaper broadband - that's a good thing isn't it?
The Government is concerned that if the price is too low and means customers will keep using copper rather than the UFB network, it puts the main operator, Chorus, at risk of failure.
How has the Government responded?
In a recent discussion document it recommends a far smaller cut. So broadband prices will fall, but less than under the Commerce Commission's proposal. The Coalition for Fair Internet Pricing says the difference is about $600 million over six years.