Found it via aa.com. It's bookable, but the price is different. It shows USD 1022 all-in with same flights and same fare basis.
Maybe ITA is wrong this time (or lost some of the taxes around, since the fare basis is EUR 450 for both ITA and Iberia.com; AA shows USD 967 + USD 54 in taxes).
I managed to get to the rules, too, via aa.com. If anybody finds a way to book the 555 EUR fare, please let me know.
Thanks again!