A French website and a radio station, quoting anonymous witnesses and an anonymous email, have suggested that the Koh-Lanta production team reacted slowly because Babin's illness was initially regarded as good footage for the show.
The reports have also suggested that Babin was taken to hospital by boat, rather than plane, to save money. Koh-Lanta's producer, Adventure Line Productions, has threatened to sue for libel.
The production company has turned over film of the incident to French investigators and insisted that it proves safety procedures were respected.
Jeremie Assous, a lawyer representing Babin's family, said he was convinced his death could have been avoided.
Another witness came forward to deny that there had been any delays in treating Babin. Guillaime, 23, another contestant on the show, told RTL radio: "Gerald was shooting and suddenly felt weak. The doctor arrived very quickly. He did everything you would expect in a very professional way."
Koh-Lanta is one of the most popular programmes on French TV channel, TF1. The president of TF1, Nonce Paolini, said that media which had "peddled anonymous reports" should "examine their conscience" following Costa's suicide. Independent