It would have been 1st and goal. Texas was moving the ball at will at that time so it's not like it was doubtful they would score.
The score also rushed the extra point and gave USC time enough to get a field goal. That is a 4 point swing.
If USC had held Texas to a field goal then it would have used up the clock and USC would not have had enough time to get a field goal right before the half.
Either way, it works out the same.
I agree with your logic.