Horrified co-contestants and crew rushed to try to save him but could not find him in the murky waters of the lake in the Thai capital of Bangkok, where the show was being filmed, according to Aslam, who was recounting reports of those on the scene.
Divers later recovered the body of Khan, she said.
The death came during filming of the show's 10th episode on Aug. 19, but it was not publicized until Khan's body was returned home to the southern Pakistani city of Karachi.
Thai police were investigating to determine whether the death was an accident or caused by negligence, Bangkok's Kom Chad Luek newspaper reported earlier this month. Police could not be contacted Sunday to say if the investigation had been completed.
Unilever Pakistan accepts no liability for Khan's death, Aslam said, but added that the company is in discussions to provide for Khan's wife and four children "out of rightness."
A close friend of Khan's, Babar Jumani, said by telephone that the family was not ready to talk to the media, and he declined to comment further.
Khan had already been eliminated in the as-yet-unnamed show's previous rounds, but had returned for a special challenge to earn a spot in the finals.
Plans to air the reality show - intended as a promotional tie for Unilever's Clear shampoo - were on hold. Aslam said Unilever Pakistan, a division of the multinational soap and cosmetics maker, was not involved in the production of the show, which was handled by a director and crew from the Indian entertainment capital of Mumbai.
Reality television shows often subject contenders to harsh physical challenges.
In May, a contestant of the Bulgarian version of "Survivor" died of a heart attack while filming on an island in the Philippines. Noncho Vodenicharov, 53, collapsed after finishing an unspecified activity for the contest, Philippine police said.