An Unanswerable Question

The philosophical question in Poul Anderson's "The Barrier Moment" is: how do we know that the universe did not recently appear complete with false memories, records and evidence of a long past? If the question is unanswerable, is it meaningless? Does it matter? Would a time machine answer the question?

We, or at least I, forget many details so that an experience is remembered without most of its background. We know that many memories are constructed and can be erroneous. But surely some memories feel like direct acquaintance with past events? To remember is not to consult a set of records. I see something, then I remember seeing it. Will you, in a few moments, doubt whether your experience of this moment occurred?

Poul Anderson constructs a (very) short story out of this question but, of course, it does not really go anywhere. Some sf is like that: one idea in a few pages or less. Asimov has one where a drunk claims to be a time traveler who knows what killed the dinosaurs: the little ones with guns killed the big ones, then each other. And so on.