Unless she lied in her first e-mail, which it doesn't seem like she did, the reason she made those demands is because they asked for a retraction of the paper without indicating why the paper should be retracted.
Asking for the identity of people that have the authority to ask for a withdrawal of your research without stating their issues with it seems understandable, if excessive.
Dean's statement is clear that it was approved before being submitted:
> Unfortunately, this particular paper was only shared with a day’s notice before its deadline — we require two weeks for this sort of review — and then instead of awaiting reviewer feedback, it was approved for submission and submitted. A cross functional team then reviewed the paper as part of our regular process and the authors were informed that it didn’t meet our bar for publication and were given feedback about why. [...] We acknowledge that the authors were extremely disappointed with the decision that Megan and I ultimately made, especially as they’d already submitted the paper.
There is no statement at all of how to reconcile "approved for submission" with "didn’t meet our bar for publication", which probably means that there is no reconciliation, and the cancellation was done outside normal process.
I wonder if he is trying to say that there was a process error, it was approved without review (in error), she sent it out, and then they came back to her and said "wait, no, you can't publish that after all"
Asking for the identity of people that have the authority to ask for a withdrawal of your research without stating their issues with it seems understandable, if excessive.
But maybe I misunderstood something.