In Sherlock season 4, episode 2: "The Lying Detective", two nurses incorrectly assume Sherlock writes his blog himself, which John later corrects. Even Smiths daughter makes the same assumption. Why is that?
Like @paulie_D says, its a joke. The idea being that Watson gets no credit for his work, even though he is critical to Sherlock's success (which was the subtext of the episode).
You can see Watson trying to explain to people that it's his blog the first few times. Later on, he just gives up and rolls his eyes when someone congratulates Sherlock on his "blog".
Well, I did some research. Apparently, this is meant to be a reference joke.
Once, Sir A.C. Doyle was on a boat. The boat was rowed by a Cornish boatman. When the boatman come to know about the author's identity he exclaimed, ‘Sherlock Holmes stories were never quite the same after he came back from the dead’.
In the episode, the Nurse (Katy Wix) is given the name Cornish as a reference to Sir A.C. Doyle's critic, the Cornish Boatman.