I think what got me going on the idea was the fact that if he was such a well known, first class detective, borderline celebrity as it were, it seemed strange to me that Lestrade didn't seem to know who he was.
In this show's universe, Holmes doesn't seem well-known at all, at least not in the US. In season 1, none of the fellows had ever heard of Holmes until Watson told them about him.
And it makes sense, since there's no indication that this Dr. Watson has ever published any tales of his adventures with Holmes. And it's not like Holmes ever sought publicity for himself, being content to let Scotland Yard take the credit as long as he had the satisfaction of solving mysteries and helping people in trouble. So it's understandable that this Holmes would not be all that well-known outside of the British or European law enforcement community (and criminal community). I do find it a little implausible that Lestrade has never heard of him, but it's consistent with the precedent within the show, so I chalk it up to a questionable writing choice rather than evidence that Holmes is unreal.