Is Predators really the true sequel?

So, I've watched the review of Predators by the AtTheMovies guys... I've also read a couple online. It seems to be the consensus that Predators is supposed to be the true sequel to Predator and not Predator 2. Since I haven't seen the latest movie in the franchise, I can say for sure what I think, but I'm told there are references to the first movie's outcome.

I want to know why the writers decided to completely forget all the other Predator-related movies. Correct me if I'm wrong, but in Predator 2, more than one person was left alive that knew the predator was here on Earth. Mike Harrigan and Garber survived... did they really just keep their mouth's shut? How did Mike explain the giant hole in the ground left by the departing Predator ship to his commanding officer? I'm going to assume that Garber works for the same agency as Isabelle in Predators, therefore it makes sense for him to keep the predators a secret, but I find it hard to believe no one else spilled the beans. I guess piles of dead bodies left behind by the predator isn't enough for people to start asking questions... especially considering how these faceless victims died (horribly, I'm sure).

I can understand wanting to distance yourself from AVPR, but at least try to be consistent with what we know already. Like I said, I haven't seen Predators. I'm going on what I've heard about the new movie (novel idea on the internet, yes I know).

Oh, I picked up Predator: Ultimate Hunter Edition on Blu-ray. Pretty good transfer considering the age of the film. Other nerds on the internet are complaining of waxy-looking images at certain scenes, notably Dillon and Dutch at the beginning of the movie while look over the map and discuss the up-coming mission. I noticed how Dillon looked a little fake, but it certainly didn't look as horrible as some would have you believe. I own the DVD release, so this is a huge step up as far as I'm concerned.