Ahmen's only offense is that she acted a bit carelessly in the quest to build her brand. The unforgiving coverage and backlash she's received since, I believe, has taken away from the real cause for concern here, which is news distributors and reporters believing that picking up tweets from journalists somehow absolves them from their own duty to double-check facts before running a story.
I don't think Prince Andrew is a serious threat to the survival of the House of Windsor. Even as the Queen's second son, he's pretty low down the succession pecking order, below Charles, William, the infant Prince George and Harry. And after all, our history is littered with princes behaving badly. The real threat to the family firm is Andrew's big brother.