12,000 might be pushing it a tad, but if you don't think there will be more than the allotted 3,800 tickets, you are plain crazy.
I imagine the claim that every Texas fan who requested a ticket allotted to their ticket office got one is probably accurate. The thing is, this is the number 2 team in the nation, one of the most storied franchises in college football history, and the pride and joy of the third largest state in America. These fans get out and travel for the Horns, and I imagine the majority of these fans made the decision to search for better seats than a second deck, south corner view. My guess is there will be a few thousand fans in the allotted visiting section, and somewhere in the neighborhood of five to ten thousand additional Texas fans throughout the stadium. So I would guess a total in the 8 to 12 thousand range, or around 20% of all the seats.
Regardless of what the percentage ends up being, the population of Laramie with more than double on September 12th, and the War will be the largest "city" in the state of Wyoming that day. With standing room and grand stand seats, there will be over 50k screaming for one team or another, and the bars will be PACKED beyond any one's imagination!