Earlier quoted context omitted.
Admittedly English is not my primary language, but "She would have had to have been being watched" seems to be a construct used in a class, but not something you would hear in day-to-day English.
Obviously the situation is fairly rare, but it sounds like a perfectly natural thing to say when it's true. I don't think it's an artificial example at all (whereas e.g. no-one actually says "buffalo" as a verb).
It doesn't sound natural to me at all; it sounds incredibly awkward to me. In a situation like that, I think people would say something like "someone would've been watching her at that moment".