The "America's Got Talent" judge told The New York Post that she's quitting the show because NBC fired her son, Jack Osbourne, by email two days before he was to co-star on the reality show "Stars Earn Stripes."
Jack Osbourne, 26, was diagnosed recently with multiple sclerosis.
In a statement Monday, NBC Entertainment Chairman Bob Greenblatt said the network "does not discriminate on any basis."
All potential contestants for "Stars Earn Stripes," which puts celebrities through arduous military-style exercises, had to undergo medical vetting, Greenblatt said. He cited medical privacy in declining to discuss Jack Osbourne specifically.
"Stars Earns Stripes," which debuts Aug. 13, requires "dangerous water stunts, strenuous physical activity, and uses live ammunition," Greenblatt said.
Jack Osbourne was offered two alternative roles on the show but declined both, said Greenblatt, who made an effort to smooth things over with the Osbourne clan, including patriarch-rocker Ozzy Osbourne.
"We have the deepest affection for Sharon Osbourne and consider her to be part of the NBC family," Greenblatt said. "And our hearts go out to her, Ozzy, Jack and his family at this time."
NBC declined further comment. Sharon Osbourne's publicist didn't respond to a request for comment.
A person close to the production said that, contrary to Sharon Osbourne's claim that Jack Osbourne was abruptly fired, NBC hadn't signed him to a contract and had tried to call Sharon Osbourne several weeks beforehand to discuss why her son wouldn't be on the show.
An email was sent after she didn't respond, said the person, who was not authorized to comment on the issue and spoke on condition of anonymity.
Sharon Osbourne had tweeted two weeks ago that she wanted to leave "America's Got Talent," but gave no explanation other than saying it wasn't an issue of money. She remains under contract with the talent contest, the summer's top-rated series.