[lmm]

> If you're talking about being watched at a particular moment

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.

[dataflow]

You're not going to get across the notion of an organization doing the "watching" sinisterly without additional context, at which point you don't need this awkward wording in the first place. Mind you, you yourself described the meaning as "someone was continuously watching her at the time". That's the natural interpretation of this sentence. I can't speak for BrE I guess, but in AmE the wording is quite jarring, and people would not opt for this wording when they could add "someone" or some other subject and make it sound so much more natural than awkwardly forcing it into passive voice. ("Someone would've been watching her", "someone would've had to have been watching her", "they would've been watching her", "they would've had to kept her under watch/surveillance", etc... the list goes on...)

[lmm]

> You're not going to get across the notion of an organization doing the "watching" sinisterly without additional context

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.

[dataflow]

>> You're not going to get across the notion of an organization doing the "watching" sinisterly without additional context

> 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.)

[lmm]

There's nothing jarring about the sentence though. It's just normal English. The difference between "she's being watched" and "someone's watching her" conveys the same meaning that it would in any other sentence.