Cox has said he was asked to re-record his accent for his character Magnus Bain because viewers would not understand it.
The Dundee-born star said: "I thought I'd conquered the accent pretty well, and even learned some old Shetland words, but I had to re-voice my part because they said my accent was too strong for the average audience to understand.
"This was not an artistic decision; it was a BBC decision to please a certain audience. I was extremely affected by it, it bothered me a lot, because I didn't think it was fair on those who have that accent or other regional accents who pay their licence fee.
"That shouldn't have happened in a BBC Scotland drama. I pointed out that they didn't dub the Scandinavian crime drama The Bridge, they had subtitles, so why couldn't they subtitle Shetland?"
Speaking to an audience at a debate in Glasgow, Cox said: "The BBC is feudal. People come up to Scotland to better their careers here. There's a BBC mentality based on careerism, where certain things are not being decided until after the Referendum, because politics permeate everything."
The star of Hollywood films Rob Roy, Braveheart, The Ring, X2, Troy and The Bourne Supremacy, who lives in New York and Edinburgh, said he would come back to live in Scotland if there is a Yes vote in September, and that he admired the SNP Scottish government even though he was a member of the Labour party.
He told the event on independence and the media at the Centre for Contemporary Arts: "We have seen the failure of the democratic process at Westminster, and I see the way forward as a United Federation of Britain rather than a United Kingdom. The referendum is an opportunity to start again, to get back to who we are and what we believe in.
"After a Yes vote I would come back to live here and help build a new Scotland."