Another native English speaker here. This would be how I would parse "She had to have been being watched," but I think it's not quite the full picture in this sentence's case. It's important to note that the "would" adds the implication that this conclusion is being drawn based upon some other (possibly unspoken) observation or proposition.
I would say the meaning is probably closer to "In order for some unspoken condition to be true, it must also be true that, during the moment of time in the past about which we are speaking, someone was watching her."
Ugh, I have to admit it seems technically "correct" after all :-) but with such a painful (and uncommon) sentence structure that it makes you question if it's right...
There are subtleties involved, but the most basic use case is that the former refers to an action that took place before some point in the past (to which the sentence refers), while the latter refers to an action that was still happening at that past point.
[1] https://en.wikipedia.org/wiki/Uses_of_English_verb_forms#Pas...
[2] https://en.wikipedia.org/wiki/Uses_of_English_verb_forms#Pas...
Essentially it means “it must have been the case that, at the moment we’re speaking of, someone was watching her.”
Your sentence is slightly different, in that it implies that, in general, someone was watching her during the timeframe we’re talking about, but not necessarily in the exact instant we’re talking about. Also, like the example above, your version could mean she’s someone who in general is watched (like the person who generally lives in Berlin), as opposed to someone being watched right during the instant we’re talking about.
Complicated!