It's not just petty vindictiveness, Moira made it clear that no precogs should be allowed in Krakoa, so while she has a personal reason to be pissed at Destiny, there's something about the future that she doesn't want the rest to know, and while she claims it's that "we always lose":
https://i.imgur.com/mtEUDi6.png
https://i.imgur.com/nMNOu9t.png
(PoX#6)
I think there's more to it than just that...
You're remembering correctly:
https://i.imgur.com/gVdhojE.png
(HoX#2)
Man, for a place with telepaths, Krakoa has terrible security that can track who's teleporting where, Krakoa has terrible security...
Like fuck, Mystique just walked in, got Cerebro, told Hope to resurrect some mutant and, instead of putting it back ASAP, just decided to let Hope keep it for a while? What the hell? Lol
That sounds like an infinitely looping bullshit that would basically allow her to copy the others of anyone within the universe eventually lol.
From what I've seen in older comics, she can see the future with scarily good predictions, but essentially becomes blinded if something isn't supposed to be there, which's what happened in Days of Future Past, she could predict anything the X-Men were doing, except Kitty, who had the whole mental time travel going on, with her future self being in her own body.
Later on in in X-Factor#8, Jean was another interference:
https://i.imgur.com/OMg36Bx.png
But I have no idea why, might've been explained later.
In Krakoa, Moira is confirmed to be one more or less, since she said she can't actually see Moira, but can see the events around her, but Destiny can still find and kill Moira if she wants to, though that would cause a reset, unless Moira is depowered
That makes me wonder, did Rachel and/or Cable ever mess with her predictions? 'Cause logically they would, at least at first.
Anyways, I don't like how the security is so sloppy here, it's also odd how Xavier and Magneto got so desperate they thought revealing everything to Emma was a good idea, which, considering how much a wild card Emma is, that is a risky bet to make... That also makes me think of the first issue where Emma is the one resurrecting Xavier and Magneto, now that we know that she knows about the other timelines, she could use that chance to do something to them when they eventually get resurrected.
Really like how Hickman writes Destiny, she's just so, imposing.