The claim was made by the husband of one of the people convicted of the killings.
David Stewart's wife Hazel, was convicted of killing her former husband Trevor Buchanan and Lesley Howell.
Lesley's husband, Colin Howell, was also found guilty of the double murder.
Mr Stewart said the Buchanan children were not given an opportunity by ITV to view the drama before it went to air.
ITV's The Secret tells the story of convicted killers Colin Howell and Hazel Stewart, then Buchanan, who killed their spouses and kept the deaths secret for 18 years.
ITV said the families were offered a chance to view it before it aired.
David Stewart said he understood the Buchanan children were not contacted.
He contacted BBC Radio Ulster's Talkback on Friday to make what he believed was a correction.
Presenter William Crawley said: "He's referring to that statement (from ITV) I read out a minute ago and says that Lauren Bradford [Lesley and Colin Howell's daughter] asked for a viewing and that he understands that's where that came from, that claim from ITV.
"David says Trevor Buchanan's next of kin were not given that opportunity and that he supports Lauren's position in all of this."
Howell and Buchanan are serving jail sentences over the murders of Trevor Buchanan and Lesley Howell, whose bodies were found in a fume-filled car in Castlerock 25 years ago.
Police believed at the time that they had died in a suicide pact, but in 2009 Howell handed himself in, admitting that he had gassed the pair with Hazel Stewart's help.
Years after the killings, she married David Stewart.
The programme has been criticised by Lauren Bradford, who said it had left her traumatised.
Lauren Bradford wrote an article in the Guardian after the first episode of The Secret was broadcast, saying its makers "trivialise the reality of these events and dehumanise the impact that it has on those involved".
She added that victims' families needed to have more rights "over their 'story' and the narrative of their loved ones".
ITV said The Secret's scripts were based on an "exhaustively researched" book by a "highly respected journalist" and that extensive extra research had been carried out.
It said the families of both victims had been informed of the production and given an opportunity to see it before it was broadcast, but added that it "never suggested" they had "approved or authorised the drama".
On Wednesday, Prime Minister David Cameron said he would hold a meeting with the culture secretary to discuss the The Secret.
It followed an intervention from the Sheffield MP Louise Haigh who raised the issue in the commons.
Lauren Bradford is Ms Haigh's constituent.
Ms Haigh said the victims' families were reliving the pain of their loved ones' killings as a result of the drama.
Mr Cameron said he would discuss the programme with Culture Secretary John Whittingdale to see if there is anything "more that can be done" in similar cases.
Actor James Nesbitt plays Howell in the drama, which is based on a book by journalist Deric Henderson that details the murders and the years that followed.
The children of one of the victims of a double murder in Castlerock in 1991 were not given a preview of ITV's drama, The Secret, based on the killings.