In our case it wasn’t in the theme folder, it was in the root “wordpress” directory replacing the correct index.php. I guess I must have uploaded it wrong, but the strange thing is that I did one mass upload of wp-content, and every other file is in the right place. Weird.
I am not sure either, but it happened to us as well. Upgraded a blog with no issues, the second one had the exact same problem as yours — and there it was, the index.html with the same “Silence is golden.” comment. Thanks for the tip, we were getting worried and, like you say, it’s quite easy to solve once you know what it is.
If it’s a joke of some sort, it’s not funny at all.
Thanks again, davert!