Here is a map of the center boundaries from Wiki. ZDV being Denver, ZMP being Minneapolis. Boundary between is basically right down the middle of Nebraska.
http://upload.wikimedia.org/wikipedia/en/8/8e/Tfrmap.jpeg
Looking at that, I would say that MSP approach would have been totally out of the loop until it became a concern that there might possibly be an emergency of some sort.
At 37,000 the flight was never in their territory. Even with the knowledge that the flight was an inbound, they would probably look at the target and think he was diverting to O’hare or something.
