For what it's worth we ate at Flying Fish on a Monday evening last May and everything was quite good. Better restaurants typically get their seafood fresh on a daily basis, especially on the coast.
With the amount of guests being fed at WDW I have a hard time believing at their signature restaurants, especially, that the fish wouldn't be fresh. We encountered this very problem at Artist Point one night when we wanted to order the Copper River salmon and it was unavailable for the evening because they weren't able to obtain any that day.
Now, since Fulton's isn't a signature restaurant maybe you have more reason to be concerned ... I don't know since we've never eaten there. But I don't really think it's anything to worry about.