Interesting. It's hard to say with the facts presented, it wouldn't make sense for the fight to have occurred near the Fire Cavern. And yet there no visible mountainy areas inside Garden.

Unless Squall went early to train a little before hand and ran into Seifer. And the SeeD (probably Quistis), was going to show later but got the call from the infirmary. Or maybe it was Quistis who found them.

The doctor person only said that the injury wasn't serious and to come pick up her student. So Quistis seemed to already know.