Also, if this was a hoax, I would have found at least one site on the Internet refuting it.
Not necessarily. It would take some effort and expertise to be able to say absolutely that either a) Saint Nilus never wrote or said anything of the sort, or b) that this quote was written in so-and-so's basement a few years ago.
It's easy for me to suspect that it's invented, but would be quite difficult and time-consuming to prove that it's invented.
It's also a question of whether this alleged prophecy has risen to the level of importance to get someone's attention to search out it's authenticity.
Since it's not a matter of dogma or morals, any Catholic is free to believe it authentic or not. My own personal opinion is to doubt it.
Now, if someone would give me a page number from Migne, or something, I'll reconsider.