Strictly speaking you're correct -- a distributed snapshot doesn't capture the state of the system at a single instant. But there's a sense in which the nondeterminism introduced by the snapshot is no worse than the nondeterminism that is intrinsic to a distributed system.
To be more precise: any "possible outcome" of the snapshot was also possible at some point during the original execution. And likewise, any "impossible outcome" of the snapshot was also ruled out at some point in the original. So if viewed from the outside, the fact that you took and restored a snapshot is indistinguishable from the normal situation of having an asynchronous network. It can't cause the system to exhibit any behaviors that weren't otherwise allowable.
(Apologies if I'm just restating what you already know; other readers may not be aware of it. This might be the same property that you're calling "integrity".)
This is reminiscent of one of Scott Aaronson's comments from the original article. If quantum effects are significant in the brain, then it's impossible -- even in principle -- to "perfectly" copy it such that the original and the copy are guaranteed to behave identically. But if the original and the copy are statistically indistinguishable, it amounts to the same thing.
