>You would think if she were not telling the truth, she would have given up by now...
What might be happening here, to be charitible, is that the former Miss Altamore may well have been brought up believing that she WAS, in fact, a Lusitania survivor. In which case she would have no reason to give anything up. But, the similarities between her story and that of Barbara McDermott are, as Mike pointed out, disturbing.
It is just within the realm of the possible that she slipped through the cracks in 1915. One rather interesting case that highlights how....harried....things were, post disaster, is that of a passenger who Cunard classified as "Dead." A rumor reached them, a few months after the disaster that he was, in fact, alive and in Italy. But, inquiries in Paris and Queenstown showed no record of his having travelled to one from the other, and after exhaustive correspondence between various constabularies, embassies, and Cunard Queenstown, Liverpool, and NY, he was declared, ca. December 1915 as unquestionably dead. Then, from Cunard's office in Antofagosta came seemingly irrefutable evidence that the dead passenger was truly alive and well in Italy. At that point, someone at Cunard Liverpool came up with the brilliant and previously unexplored tactic of writing to the passenger's wife, who lived in the U.K. Within days it was confirmed that this man HAD survived and managed to travel from Queenstown to England, and then on to Italy via Paris without registering with a single authority and leaving not a trace- other than an extended newspaper interview that Cunard apparently never saw- that he survived. And so as late as January 1916 the matter of who lived and died on May 7th was still not entirely resolved.
That said, it is so far from probable that an entire family could slip through the cracks and leave no trace, that it is hardly worth mentioning. I suppose, if one wanted to be efficient, one could check the State census from June 1915 (They are held in mid-decade and not as easily accessible as the national ones) to see if the Altamore family was still settled in the US at that point.