Alitalia "sale" seems to have sailed; and does Priceline really sell airfares with "no fees"?

So we were poking around this Alitalia spring sale to Italy.

Couldn't for the life of us find any seats at the lowest advertised prices. For example as you can see below, New York to Rome is supposedly $349 RT including all taxes and fees. Best we could do from the New York area was Newark to Rome for $464 RT. Not a horrible fare, but not $349. Let us know in the comments below if you found anything better, or if you confirm our results.

Just for the heck of it, because that's the way we are, we tried, same dates and flights. Because Kayak automatically preselects as a search method, a Priceline search popped up (annoying, we know, but that's how they make their money, right?).

Priceline informed us that this was a no fee airfare:

$485 RT all-in for spring travel, or $21 higher. Now, $21 isn't a lot of money, but is there a fee built in there, or is Alitalia selling for less than with online travel agencies. We don't know, but obviously you might as well book directly with Alitalia, capisce?

Anyway, we saw this Alitalia sale advertised in our Sunday New York Times so we thought we'd give it a look-see, but it looks like it's pretty much sold out at the lowest fares. They also have a summer sale to Italy for travel May 26 to Sept 9.