What is "the show"? I suppose each can have a different definition of what "the show" is, I can only give mine.
"The show", to me, is everything involved on Saturday afternoons in the Shoe. The team, coaches, band, historical Ohio Stadium, and the fans/students/alumni in attendance. Each of these is singularly is not "the show", it is all put together that makes "the show".
All items that for me constitute "the show" also, on some level, illustrates what it means to be part of the Buckeye family. I believe that JT stresses with his players that they are part of something bigger than themselves (or the football program for that matter), that they are part of a huge and vast family...The Ohio State family.
So while I believe that fans at a game are part of "the show", singularly they are not "the show". A prospective recruit that would be swayed to OSU simply due to game atmosphere doesn't, IMO, get what it means to be a Buckeye. And maybe that is why JT encourages those recruits who are swept up in things during an official visit during a game, and want to commit on the spot, to go home and think about it a little bit.