I do see this as a kind of Death of an Ideal - the ideal that humanity can know everything there is to know about the universe. Scientific observation, unfortunately, has its limits. But this is not a new, pessimistic development in physics, nor in science in general - It was probably depressing 100 years ago to find out that Newton's predictable clockwork universe didn't make sense.
That said, I don't personally find this limitation to be saddening. I am content with knowing only what I can percieve affecting me, for if it does not affect me, what use would knowledge of it have? I suppose that Man, driven by fear of the unknown, might desperately seek to fill the void (and be frustrated to find out that such a pursuit is like digging a hole in mud). But curiosity does not drive me, at least, to look to the distant unknown and demand answers (the "arrogance" of the article).
If one day humans or other intelligent beings are unable to observe and collect the data necessary to come up with the Big Bang Theory this would be the death of notion of finite beings knowing the true nature of the universe.
That notion will always exist so long as the heart of human culture (curiosity, arrogance, whatever you want to call it) persists, irrelevant of what observations to which it would be applied. We look now at future people and might be sad they will not be able to share the fleeting glimpse of the universe we now have, but they will not share our depression (until they develop a theory that won't last, either). So them and us will be in about the same position, just with different science. As Soly noted, it all rounds to zero in the end.