Actually I never thought about where the fish is from. The thinking is that if it's from a good Japanese restaurant, then it must be good!
The time limit thing is really annoying, takes the joy out of eating. I mean I don't mind if it's fast foodstuff or cheapy quick in quick out places. But normally you'd like to sit and eat and chat over dinner and enjoy the whole experience if you're going to a decent place. Too bad it's become more popular, even in Japan now.