Of course you do. Consider "Do you ever feel like you're being watched?" versus "Do you ever feel like someone's watching you?" Both those sentences are natural English and in a certain sense they "mean the same"; nonetheless they convey a quite different feeling, and neither is a replacement for the other.
> Of course you do. Consider "Do you ever feel like you're being watched?" versus "Do you ever feel like someone's watching you?"
I was talking about in that example. I was not making a claim about every arbitrary sentence containing the phrase "being watched".
Understand that if you add enough contortions and make a sentence jarring enough, you won't get anything across without additional context. (To a human I mean. I guess I have to add that caveat because other you'll post another rebuttal about how a sufficiently strong AI would parse it just fine.)
But you're not; you're talking about having been being watched, something that was an ongoing process at the time (past progressive).
> And whether it's sinister or not is pretty beside the point.
People choose their phrasing because they want to convey particular connotations. So you can't just say "this is a simpler way to say the same thing" if it carries different connotations.
> I'm saying that phrasing is pretty darn unnatural English, sinister or not.
All I can say is it sounds perfectly natural to me, as a native (British/Irish) English speaker.