She sends for approval 1 day before the conference deadline, proceeds to submit the paper with conditional approval, and waits for the actual approvals. It is common practice with one side effect: if reviewers don't like certain parts of the paper, they can ask you to withdraw it (since you don't have an option to update the paper at this stage). If the paper was submitted for approval before submitting to the conference though, then they would have some room for back-and-forth engagement with updates on the paper.
Nowhere in the account of the story from the other party anything is specified as "conditional" nor whoever issued the initial approval is mentioned at all. More weirdly, in her account of the story, the "back-and-forth" came from, tada... HR department, which is super weird.
Look, I am not necessarily picking her side in the more general story, but it is apparent this paper submission story in isolation is super weird. It seems feasible that she was in the queue for getting the axe having engaged in prior fights with the company (some mention of threat of lawsuit, etc). I also acknowledge the account of story from her side was quite cherry-picked and actively strategic, if not deceitful, and it does not even seem that Jeff was a direct player in this saga. Looks the highest level person in the loop was Megan, not Jeff, and Jeff is simply dragged into the mix for the opportunity to throw a punch at his reputation. That, however, does not minimize the weirdness of putting the whole thing on this two-week paper submission policy.
I agree with you for almost everything you said. This case is definitely unusual. What I mean by conditional is that the person who approved it initially is not an actual reviewer.
For your last sentence, I think Jeff uses that 2-week policy to state that his position is "technically" right.