Here is the thing that apparently not many people truely understand......You can not have a 100% accurate stat weights for everyone because what happens is with every piece of gear they change.
https://www.raidbots.com/simbot/report/rJlOfABGZ
These are my current stat weights
( Pawn: v1: "JADAWIN - Beast Mastery (Raidbots)": Class=Hunter, Spec=BeastMastery, Agility=24.73, CritRating=23.19, HasteRating=30.23, MasteryRating=27.07, Versatility=21.36)
So mine currently are Haste > Mastery > Agility > Crit > Vers
The thing is that is in no way, shape, or form indicative of what your stat weights would be or should you use the values that are in that sim for yourself. What people really need to do is just start using raid bots if they are not super familiar with SimC and start working on understanding how each piece of gear impacts your weights and the expected return on them. I have done some SimC work with the PTR model for trying to find a BiS list and have come up with
Haste = Mastery = Agility = Crit > Vers on some iterations
So really its about your particular gear. To make statements like "They arent that close" honestly are just annecdotal to perhaps your gear but that statement is 100% right and 100% wrong at the same time depending on who is simming thier current gear. What we need to start doing as a community is stop trying to box everything up in a 1 size fits all statement because that will rarely be accurate. What would be accurate is to teach people to use the tools that we have available to us to come to the right choice for them individualy concerning gearing and stat choices.