JUST IMAGINE IT.
This will make your day better… promise ;)
I’m 827% positive that the reason Anderson doesn’t think Sherlock is dead is because Sherlock purposefully let Anderson see tiny glimpses of him the past several years, just to screw with his head. Appearing through Anderson’s window in the woods, standing across the street of his favorite coffee shop, leaving small traces of his presence in his office.
Because Sherlock’s a little shit like that.