Yes it says that there is no business class available on the flight.
But when there is business class actually available, i would think it books there, regardless of fare code. With this system, you first have to look up expertflyer or something to see if there is availability in the fare AY books you into (because this varies by availability in buckets, not by booking flex or classic).
Also i (or anyone else) would feel cheated if you buy a business class ticket, for business class price and get seated in economy when business class is available and has seats free.
Few days different, same exact flights and AY books into I. AA has availability in I, you get business class seat and price is exactly the same what you pay to AY.
Just doesn't make sense to me.
And this is also same on flights LAX-ORD/JFK, just random what you get.