I would not personally make that generalization. As was mentioned above, high humidity makes the wood swell (get bigger) and low humidity makes it shrink a bit. What that means in terms of curvature depends on a lot of factors. What humidity was the neck built at? Do the neck wood and fingerboard wood expand/contract faster or slower than each other? Is it a fretted neck, and how tight are the frets in the slots? And so on.
Also, I'm not sure what you mean by "same" in this sentence but I'm betting you're pretty much wrong:
Generally, luthiers will aim for as true a grain direction as they can, in terms of orientation along the length of the neck (you don't want runout). This is for strength but also to keep movement predictable. A rift sawn neck or one with a lot of runout will be much more likely to go wonky when humidity changes, compared to a neck with true grain orientation.
But - that said - there isn't consensus on using quarter sawn lumber vs flatsawn. Many luthiers prefer quartersawn, but some, including big name brands (ie Fender) use flatsawn wood almost exclusively. This choice can change what happens as a neck moves.
And further, even among "perfectly" quartersawn or "perfectly" flatsawn blanks, you have to remember that trees are round, not square. A perfectly cut blank will still essentially have some curve in the grain when viewed from the end, with an "inside" and an "outside" face (ie the face that was towards the heart of the trunk and towards the bark, respectively.) So even if a luthier is selecting only well quartered blanks, they may still end up with necks that behave differently because some were cut "face up" and some "face down."
A multilaminate neck basically averages out the characteristics of each laminate. This usually means it's more stable since you're hopefully placing the laminates so they cancel each other out. Although it's possible to build a laminated bank that acts additively if you stack the laminates all "pointing" in the same direction in terms of the grain - hopefully, no one would do this on purpose though...