I agree, Poe's reputation is only so high as he occupies a spot hard to fill by other American authors and as such is the one Romantic era prose fiction writer that almost everyone in the US is forced to read. His style is not so innovative, though his particular synesthesia is a little intriguing. If I were to look for the best shot fiction writer in the States though, my first jumps would be at Hemmingway and then at Flannery O'Connor - almost by instinct. Then if I were to say English as a whole, I would jump to someone like Katherine Mansfield or Alice Munro.
Generally though short fiction is a continental European domain. It hardly factors into American traditions outside of a brief stint in the modernist era, I think primarily because printing when American presses took over was already cheap enough to get novels out - the brief stint of modernist writing, when people like Fitzgerald or Hemmingway could toss a story out for a periodical seems the last movements of a periodical-digesting time period. I mean, how many major serialized books can we think of in the American tradition even?
Everything JBI has to say about American literature can largely be dismissed as being largely rooted in his usual anti-Americanism. Robert Hughes referred to it as the "cultural cringe"... the realization of the irrelevance of ones own culture on a given artistic genre. And the envy of the dominant cultures.
Seriously there are legitimate criticisms of Poe... but considering his impact upon Baudelaire, Gautier, and a great many European "decadents" and Symbolists... as well as Borges and a good portion of Latin-American literature, he is not anywhere near as minor as JBI (among others) would have us believe.
As for the American contributions to the short story, considering the efforts of Poe, Washington Irving, Hawthorne, Melville, Henry James, Ambrose Bierce, William Faulkner, Ernest Hemingway, Sherwood Anderson, Nathaniel West, John Steinbeck, Phillip Roth, John Barth, Flannery O'Conner, Raymond carver, John Updike, Donald Barthleme, etc... it would see that the short story is more than a minor aspect of the American contribution to literature.