If Koizumi was really watching Haruhi at that time, then I must say that is was a memory created by Haruhi-sama(
) then. Since the world was created "three years ago" by Haruhi-sama(
), it would be natural to think that all the memories from 4 years and + ago were created by the start of the world. Aka: The time when Haruhi-sama(
) thought the world was boring and so decided to create another one. So the Itsuki watching Haruhi-sama(
) when she was still in elementary school and didn't go to the baseball game yet and didn't realise that the world has a lot of people and all that it mear memory created by Haruhi-sama(
). Unless it was made willingly by Itsuki as he only went to watch Haruhi-sama(
the world was created. By that time, Haruhi-sama(
) was in her last year of elementary(namingly the 6th year).
Did you understand?