I have actually done a lot of psychological research on memory illusions, and it is totally plausible that someone can genuinely believe the origin of something is in their own mind when they demonstrably got it from something else they witnessed or heard. I have no trouble believing that is what happened here, but some Twitter critics make a possibly telling point, which is that the Gervais special is well known in the comedy writing world, and it is not likely that a room full of late night comedy writers could not explicitly recognize the source of this joke.
Song writers are often unconsciously influenced by songs they have been exposed to, but it would strain credulity if a room full of ten rock and roll musicians wrote a new song together that began with the opening riff from Smoke on the Water and claimed they had come up with it themselves.