Reports in this week had suggested that the programme would be hostile and damaging to the corporation. However, both broadcasters have denied this is the case.
A spokesman for Channel 4 said the documentary was a "considered look" at how views on drug-taking have changed over the years and that this was reflected by the high-profile cases featured in the show.
"It's about four high-profile cases of presenters with a problem with drugs, how it was handled and how it reflects changes in media and society," he said.
The documentary, called 'Snorting Coke with the BBC', looks at the way different presenters were treated by the BBC including: former 'Nationwide' presenter Frank Bough, who was fired in 1988; Blue Peter presenter Richard Bacon, who was also fired; and 'Have I Got News for You' presenter Angus Deayton, who initially returned to work within weeks of revelations of his drug-taking before being finally axed.
A spokeswoman for the BBC explained that the cases were all treated differently because of the circumstances surrounding them.
Richard Bacon was fired because of his role as a children's presenter, which she said was "as a role model for children".
In the case of Angus Deayton, she said his case was different and although he initially returned to the show, he could not continue presenting it once he became the subject of the news.
"His position on the show became untenable as a host for a satirical quiz show," she said.
Channel 4 also denied reports that it had moved the documentary after reports suggested that it was being criticised for being hypocritical.
A spokesman for Channel 4 said the show had not been delayed and had not yet had a confirmed slot allocated it in the schedule. He said, however, that some dates had been mooted and that it would be appearing at a later date than had originally been suggested.
BBC One controller Lorraine Heggessey contributed to the programme to help clear up issues surrounding Deayton.
It is understood the documentary will now broadcast at the end of August.
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