I have no idea what you’re responding to, but it sounds like you’re trying to get at the fact that Jim’s death was never mentioned in the news after the rooftop scene.
First of all, the news clip on John’s blog definitely was made under the supervision of the writers, as was the “hacking” video from Moriarty. The entirety of John’s blog (and Molly’s blog, and Sherlock’s website, and all other Sherlock-related web media) is dictated by the writers, otherwise there would be glaring inconsistencies. They don’t do the actual typing themselves, they have better things to do, but they determine the content and they obviously had to script and film all the extra “blog videos,” as well. They didn’t just magically appear from somewhere. The blog videos are absolutely fair game for clues.
Secondly, in the Doyle canon, Mycroft was not exactly involved in the “coverup of the fall.” In canon, Mycroft was not even aware that Sherlock had faked his death until well after the showdown with Moriarty. Sherlock did go to Mycroft for money and to take care of some personal matters, but Mycroft was only involved later and in a minor capacity. At any rate, in BBC Sherlock, I doubt Mycroft would have had Moriarty’s body removed, and I doubt Sherlock would have wanted him to.
Why?
Because Sherlock made a huge deal of allowing everyone to think that he was a fraud, and that Richard Brook was real. Remember this?: “The newspapers were right all along. I want you to tell Lestrade; I want you to tell Mrs Hudson, and Molly … in fact, tell anyone who will listen to you that I created Moriarty for my own purposes.”
That conviction would have been reinforced by finding “Richard Brook” dead on the roof. It would have appeared as though Sherlock had either shot him or threatened him until he shot himself, making the “manipulative fraud” story all the more convincing. In short, given his intent to make himself the public bad guy, Sherlock would have been better served by leaving Moriarty’s body on the roof for the police to find.
Yet it wasn’t in the news, and therein lies the mystery.
Also (and this is a personal theory) I feel that Mycroft’s role in the fall was more ad hoc, and more of an afterthought. He probably helped Sherlock to falsify an identity and perhaps to flee the country, but given that, as you said, the whole situation was partially due to Mycroft’s carelessness, I doubt Sherlock would have been on speaking terms with him when he was making plans to fake his death. He had Molly, who was more than capable of providing a false Death Certificate and other elements critical to the coverup (a body, perhaps?) so I doubt he needed or wanted Mycroft’s help, at that stage in the game, at least.