I like to think of a rival as someone that I despise losing to but yet respect, because they are successful and we do not get to always thump them. It is like the Cubs-Cardinals: They are the Cubs rival, NOT the Brewers, because the Cards actually win quite often.
I agree that on paper Minnesota is our rival (as my username implies), and that since we end the season with them, they are our rival.
But, it is the teams we strive to complete with on a yearly basis (OSU, PSU, UM, UW) that get my blood flowing each year. I expect to beat Minny even in "down" years.