I am definitely, DEFINITELY #2.
Sometimes when I am running long, I will look down at my garmin and realize that I am 5 more miles into my run and it felt like only 10 minutes passed.
I am going to give my opinion here, and note that this is based on absolutely zero research. I think probably most pros and elite level triathletes (and other endurance athletes) utilize method one during training (and racing). They WANT to think about their pace, and their form, and their heart rate, and concentrating on how badly they feel over a period of time helps them train better AND more intelligently.
I want to think about all that stuff too, but it's easier and more fun to just ignore it and daydream. Workouts go by more quickly, albeit they are probably more shittily executed (sometimes I cannot always hit my tempo sections in long rides and I wonder if this is part of the reason).
Honestly I think that's what it comes down to. I am a MAJOR daydreamer. Not just in training.. all the freaking time! When I was in college and I would go to the library to study for exams, my ratio of study time : daydream time was probably 70:30. That is a LOT of wasted time! However I think it also saved my sanity at the time.
So if you see me on a training ride and I don't acknowledge you, I am probably daydreaming about Kona, competing in the Olympics, climbing Mt. Everest, marrying
Someday I will have to make the switch. I think it will help me improve. However, I think that switch will happen about when I give up eating chocolate every freaking day, which is going to be never.