Katie Hopkins, a former Apprentice contestant, weighed into the debate and criticised Ms Brady, who said the exchange between Richard Keys and Andy Gray about football official Sian Massey "made her blood boil".
Appearing on BBC's Question Time, Hopkins also said Sky Sports had "lost its sense of humour" hours after Keys' wife said the broadcaster was "offside" in its handling of the matter.
Speaking outside the couple's mansion home in Chobham, Surrey, Julia Keys said: "Whether you like them personally or not, professionally there are very few who would knock them. I feel the wrong two guys were given the red card. It doesn't quite make sense in a way and it's questionable the way it has been handled. I think Sky was offside in the way it handled it."
Mrs Keys added the suggestion Ms Massey did not know the offside rule was "banter from the boys". "What other people do not understand is the dynamics that go on in the studio," she added.
Hopkins made similar comments, claiming the nation should be "proud" of its banter, which stoked a strong reaction from the Question Time panel and audience.
She said: "I think women actually don't want equal treatment. It's a tough world out there and what a lot of women are asking for, and you can look aghast at this, is special treatment. If you look at all-female shortlists for positions - is that equal treatment or is that special treatment?"
She later added: "Do we want a world which is completely void of colour? Do we want everything to be magnolia? No we don't. I think we need banter and I think those poor guys really died on their swords and have been stabbed in the back by people like Karren Brady."
Former Conservative MP Edwina Currie held her head in her hands at the remarks, while private secretary to Labour leader Ed Miliband Chuka Umunna said: "I don't think, Katie, you're doing anyone any favours this evening."