In my native dialect, statements including "had to have been being" are rather common. My friends, family, co-workers, etc. use them regularly. In fact, I recall saying "he'd have had to have been being reckless" just earlier today. All five of the other people present- both immediate family and non-relatives from this area- knew precisely what was meant. In other words, that intimidating clump of verbs passed unremarked.
Further, to andensande's point, one might be inclined to replace that god-awful monstrosity with something like "he must've been reckless." To do so would be to wipe out some subtleties of meaning from the original. A replacement like "he must've been acting recklessly at the time" feels like the same general meaning to me, but it also sounds stuffy and snobbish in tone (for all that it's probably a much more effective construction).
All things considered, every language that I've ever dealt with in any capacity has had its share of peculiarities. In hindsight, however, I don't recall Arabic, Zulu, or even Gallo-Lati... er, I mean French... having quite as few peculiarities as my sponge-like mother tongue.
"to be ing", "was ing", and "will be *ing" if I remember correctly, are actually thought to be an early borrowing of celtic grammar. Not much celtic anything was adopted into English, but there's a possibility that this sentence structure may be one of the few contributions of the celtic languages that were displaced by germanic Anglo-Saxon languages that eventually formed English.
(1) She would have had to have been observed.
is that it misses out the gerund form preceding 'observed', which alters the meaning slightly in my opinion. It's difficult to get at precisely but I feel like the original sentence has a feeling of time-boundedness around when she was observed which you don't get without that gerund. I think?
The original with "been being watched" feels like something the detective says when he first discovers the fact about watching. It has an exclamative aspect to it. There's a present sense of realization, mixed with the past sense of when the watching had taken place.
"She would have had to have been observed." is something like a lawyers distillation of what happened later for the court.
That being said, I have trouble to parse the original english sentence so I may be missing subtleties.