Ai Fiori does not do lunch on Saturdays.
I went there this morning with an OpenTable reservation, and the empty restaurant was the first sign was that I had made a mistake.
1) Ai Fiori's website has their hours in a non-obvious place (see if you can find it without backtracking; answer below*). Other restaurants such as The Modern and Eleven Madison Park and Jean Georges have their various hours easily accessible.
1.5) Ai Fiori's website has a prominent OpenTable widget at the top of the page. If you make a 12pm Saturday reservation, they will give you slots at 11:00 and 11:15. Those are reasonable times for lunches, and it's not really fair to expect guests to know that they are not in fact lunch hours.
2) There are several Chowhound postings mentioning Saturday lunches. So it is definitely the case that they stopped doing lunches.
2.5) Yelp has zero information about their operating hours. Nearest transit station? 34 St - Herald Sq (B, D, F, M, N, Q, R). Hours? No idea. (For the record, a Yelper's meal implies that Saturday lunch service was still available in January. So maybe the summer schedule is different. How am I supposed to know?)
3) The OpenTable confirmation emails were severely lacking in logistical details. Rather than providing concrete, relevant information about hours, it waxes eloquent on the availability of Prix Fixe menus. Unless it is made clear that the restaurant is exclusively Prix Fixe, that is not usefully presented information.
4) Capella Hotels explicitly states that Ai Fiori has "lunch and dinner Saturday and Sunday". OK, so much for The Setai being "A Cappella Managed Hotel".
5) Host who gently sent me away was nice, but not super helpful (he even had the gall to contradict point #3), and I'm not sure if he understood the nature of the problem.
6) "Ai Fiori has cancelled your reservation". That is a strange and unpleasant thing to see in one's inbox at the end of the day.
I just needed to get this off my chest. No, I didn't argue with the staff or anything like that. Yes, I know that a phone call would have been a good idea. But that defeats the purpose of using computer reservations.
Anyways, I detoured to Tocqueville (another frequent recommendation on Chowhound) for something quick, and that was pretty great. The best parts were the beet cannoli amuse, and the chocolate soufflé. The cheddar salad was enlightening, truly a very elegant interpretation of fruit-nuts-cheese salads. A lot of their other dishes on the menu looked good too. The staff was easygoing and helpful.
*answer: It is under "Contact Us", which is not even logical because one can want to know your hours of operation without wanting to Contact You. Web design has a huge cognitive component to it.