She needed to be face-to-face with the interviewer in order to lip read, she told the Herald, especially for a one-hour show.
"I consider all requests to meet very carefully, including this one, and I felt it was really important to take this opportunity to speak to disabled New Zealanders living in rural communities."
One of the programme's presenters, Vanessa Jibran, said it was an amazing opportunity to have the Green Party's disability spokesperson in the studio.
She said they invited her to find out what she and the Green party intended to do for disabled consumers, and to find out what it was like to be a MP with a disability.
"I think what we portrayed on Friday needed to be out there. "I thought it was worth it, she actually had some really interesting things to say."
Arrow FM station manager Michael Wilson said he challenged the idea that she took the trip all the way from Christchurch to Masterton as her work was in Wellington.
"She was going over the Rimutakas, that's the cost to the taxpayer."
Ms Mathers has also said the trip was planned in line with other work she had to undertake in Wellington.
Arrow FM is one of 12 Community Access Radio stations in New Zealand that are mainly funded by NZ on Air.
Mr Wilson said the station has a regional reach from Featherston to Masterton, and about 40 programmes representing different groups in the community.
"If we are doing a programme about disability, we know a hell of a lot of people in the disability community are listening."
He said the station didn't judge its success by how many Facebook 'likes' it had.
"We know fewer people listen to us than More FM, commercial radio works in a different way."
"We are here specifically to represent minorities, we are here for their voices to be heard."
Mr Wilson said Ms Mathers' interview fulfilled a particular need in the community. "We are doing our job if these people are represented."
The suggestion to use Skype wouldn't work in the presenters' studio environment, said Mr Wilson. "I challenge you to get three motorised wheelchair users around one computer."
The quality of video was also not good enough to be able to lip read, said John Hart, Green Party candidate for Wairarapa.
He said Ms Mathers was doing her job and was also a trail blazer for MPs with disabilities.
"She probably deserves credit for coming to visit a rural community, most MPs don't do that very much.''
He said Mr William's comments were "mean-spirited'' and the union could be focusing on other trips, like Prime Minister John Key's recent trip to open a novelty par 3 golf hole in
Queenstown.
According to the latest MP travel expenses disclosure statements, Ms Mathers has spent $13,950 on surface and air travel.
In comparison, excluding Party leaders, National's Mike Sabin spent $32,193, Green's Kevin Hague $16,293 and Labour's Meka Whaitiri $21,036.