The DUP's opponents, unlike Arlene Foster's party, say they do not fine members for speaking to the media without permission.
Yesterday a whistleblower revealed on Radio Ulster's Nolan Show that elected DUP members could be fined up to £1,000 for comments that were not sanctioned by the party's Press office.
Outspoken former DUP member Jim Allister accused the party of acting like North Korea.
The whistleblower also alleged that Timothy Johnson, the DUP's chief executive, was in charge of issuing the penalties, and described him as "God incarnate" and as a "judge, jury and executioner" figure within the party.
Former DUP Health Minister Jim Wells, who recently had the party whip removed, played down the sanctions.
He described them as being like a "parking fine".
"I don't know what all the fuss is about. This has been DUP party policy for 20 years," he said.
"By those who have had the fine - of which I am one - it's seen as an occupational hazard. You pay it and move on. It's like a parking fine."
The DUP said the party operates under a constitution and a code of conduct for its members and that Mr Johnson wrote to members "from time to time" on code of conduct matters, as required.
It said it did not comment on internal procedures and reserved the right to decide what programmes to participate in.
Sinn Fein said it did not and never had issued such fines to its representatives.
The Ulster Unionists and the SDLP also said they did not fine elected members for speaking without permission, with the UUP adding that historically it was not aware of any such penalties being used.
The Alliance Party said that fining elected members was not in the public interest.
"We trust our elected members to show judgment. The role of our Press office is to advise and support, not direct elected representatives," it said.
"Councillors, MLAs and MPs have responsibilities to the party, but are ultimately accountable to the public.
"While all parties would want to maintain a coherent party position on policy matters, that is best achieved by maximising opportunities for internal debate on policy development and effective internal communications.
"Fining or unduly constraining those who speak out on matters of serious concern is not in the public interest."
TUV leader Mr Allister said the claims showed that "totalitarianism had run riot within the DUP". He added: "Surely to goodness an elected representative who is mature and elected as such cannot be muzzled at the cost of punitive fines lest they dare say what they think?
"This is Northern Ireland, not North Korea, it is quite outstanding. I certainly wasn't aware of this policy when I was in the DUP. I'm almost disappointed I didn't earn a fine. There were probably a few occasions I would have qualified."
On Mr Johnson being described as "judge, jury and executioner", he said: "All that rings true from what I know about the internal machinations of the DUP. You won't get anyone speaking out about this - if they do they'll be fined £1,000!"
Earlier this week Sir Alistair Graham, a former chairman of the Committee on Standards in Public Life, described fining political representatives for their views as "authoritarian and draconian".