"I feel badly how this whole thing transpired this week," McDonald, 45, said in an exclusive statement to PEOPLE. "I had a wonderful time working on Chelsea Lately. My words were taken out of context and I'm sorry if they hurt anyone.
"That being said, I never sold or traded stories about Chelsea Handler to benefit myself," she continued. "That is not true. It never happened. It is a devastating accusation that I emphatically deny."
During an appearance on last Tuesday's episode of the Allegedly podcast, McDonald, who worked with Handler from 2007 to 2014, said that while she "enjoyed her time" working on Chelsea Lately, she also was worried about getting fired.
"I mean something would happen and my heart would be beating and I would be like, 'Is this it?' – you know? And then somehow I just managed to keep surviving."
McDonald also said that she felt that Handler, 40, was "missing out" by downsizing her group of friends and that she found out the show had been canceled after reading about it on Twitter.
The same day the podcast was released, Handler fired back at McDonald during an appearance on Howard Stern's SiriusXM radio show, claiming that McDonald sold stories of Handler to a celebrity gossip magazine in exchange for her photograph appearing in print.
"I could have fired her. I did not fire her. She had a job for four more years. I never hung out with her personally again. So I hope she was living in fear," said Handler. "It's not an internment camp. If you're living in that much fear, go get another job.
"I just thought it was a betrayal … I wasn't paranoid, I just withdrew from that whole social scene – I withdrew from her," she continued. "I wouldn't hang out with her, I wouldn't be alone with her. You know, she's somebody who would love to hear about Jennifer Aniston's house on the weekend. I could never, ever share my personal life with her again."
Meanwhile, Allegedly hosts Theo Von and Matthew Cole Weiss responded to the drama surrounding their interview.
"It's a shame that things have gotten so nasty," Weiss said to PEOPLE. "I believe Heather is a good person and her honesty and candor had the best intentions, but at the same time, what was said was said."
"Heather's words may have been taken out of context, but she shouldn't feel she has to back pedal," Von said. "They are both extremely talented."