In my five years working in pro personnel with the
Cleveland Browns, one of my jobs was to scout upcoming opponents and create that advance scouting report. So while the Browns would be preparing to play, say, the Bengals, I would be looking ahead to the next week's game against Pittsburgh. I would study the film of the Steelers, looking for formations, tendencies and anything that might help formulate a game plan.
On Sunday, while the Browns were in Cincinnati, I would be in the press box in Pittsburgh.
This is a common practice and league bylaws actually state that no team shall prevent a member of an upcoming opponent from attending a game in that capacity.