I've read Ellen's opening chapters, and there's no way I would call them omniscient. For a start she has one person per scene, and she doesn't slip into anyone else's viewpoint, and writes firmly from inside her characters' heads.
K's justification of why Ellen's novel started in omniscient was to do with the characters thinking about their past in order to deliver backstory. K said that we don't often sit around thinking about our pasts in a coherent fashion, and she does have a point. But does that make the POV omniscient? I don't think so.
In an omniscient viewpoint, anything goes. The writer can move from head to head at will -- of course this should always be done for a reason, or the reader can end up dizzied or confused. But the reader *does* move heads throughout a scene. The author can jump in and give an insight that none of the characters know, for example: What none of the characters knew was that everything was about to change...
Or the writer can jump forward into the future and point out something that would happen at a later date. The author can address the reader: Dear reader... This is called "authorial intrusion" and is a perfectly legitimate (if dated) device in an omniscient viewpoint, and one that I cannot stand! When I'm reading, I become the main character; I am in the story; I am experiencing it: all those terrible things happening to the main character -- well, they're happening to me. Authorial intrusion reminds me that I am not the main character, and in fact that I am the reader, and I'd better damn well stay on that side of the page! It completely interferes with my enjoyment of the story.
The other thing to say about all of this is that the way we represent thoughts on the page is not really how thoughts are in our head. I know sometimes mine are an almost incoherent jumble, as my thought-trains switch tracks, derail, get overtaken and stall. Thoughts on the page are a representation of what the character is thinking, and while K's representation may be closer to the truth, it's still a representation of how we think thoughts are -- just in the same way that dialogue is not the same as how we really speak -- it's more like how we think we speak.
Ellen saw what she'd done as a judgement error rather than POV error. I agree that it isn't a POV error. A POV error is when you slip into someone else's head when you shouldn't. Or when you move outside the perspective that you're writing in -- so if you are writing in an intimate viewpoint, where you are inside your character's head (as in third-person intimate, or first person), you can't say that your point-of-view character had a beatific smile on his face, because he can't see his own face. You could of course say that if he were looking in the mirror, but that's cheating. You can say he smiled. Or that he felt beatific -- even better, you can show it.
Ellen is writing a story with a big scope. She has parallel plots, so is tracking the journey of two main characters. If she were to use the type of very close POV that K favours, where thoughts are detailed and go on for paras, instead of a 120 k novel, she might end up with an extremely intimate account that spreads over 250 k and that is imminently unpublishable just because of its length. (Yes, publishers do occasionally publish books of this length, but rarely rarely rarely first time authors just because it's prohibitively expensive and the risk on a new author isn't worth it.)
The scope of our novels do, to a certain extent, dictate just how close our POV can be, as does whether a story is plot or character driven. If you're writing a literary short story where not much happens, you can afford to have pages and pages of thoughts -- in fact, stream of consciousness stories are exactly this. I can't say I particularly enjoy these, but it's horses for courses. Some people love them.
In the end, the labels we give things like POV don't really matter, but they are a way for us to check that what we does works, a way for us to understand why doing this particular thing (showing the beatific smile) doesn't work, and why we should change it.