If that's the case then I can see why there's so much arguing about NTR. That's a pretty meaningless distinction to most people I would think. The only way to avoid "catching them" is to intentionally avoid going there when they're doing it, which means you know it's happening or you wouldn't know to avoid it and you'd be bound to eventually stumble upon the scene at random.The question was not if it could be prevented that that other people have sex, but if NTR was avoidable. Sure, NTR means to lose a loved one (which Ann at this point isn't) to someone else, it means that the protagonist watches them and suffers. People usually ignore that point about the 'loved one'. But all interpretations of the term have in common that the protagonist actually has to catch the other couple. So if he doesn't, it's not ntr.
That's like seeing your next door neighbor walk out the door of your house just as you get home from work and see your wife just stepping out of the shower as you walk in. You didn't actually catch them doing anything but you know damned well what happened. You could make sure to come home late every day to make sure he can give her a few extra pumps every day while you're at work without "catching them", but you know damned well what's going on even if you never see it actually happen.
That's the part that matters to most people I would think, but maybe I'm wrong.