I buy Akagi doing this, it feels like something she would do as a character. Certainly doesn't make her "right" by any means; it's more of a self justification along with a "sorry, but:" non apology demonstrating her opinion of herself is more important than the views from others.
And I also buy this giving E pause, not for more than a few seconds of course since it falls apart under any scrutiny as demonstrated in the comments. With her position as a well-known entity in a former enemies and allies combined fleet as well as a sole survivor she's used to dealing with both sides of the fence and has probably had to mediate similar sour relations. Survivors guilt probably factors into it too with what happened to Yorktown and Hornet. Now if she entertains this for more than a minute or two that'd be a little naive and silly, but this makes sense for my interpretation of her character I think.
