According to the radar track:
FlightAware > United Air Lines #967 > 20-Jul-2010 > KIAD-KDEN
the diversion turn begins about 1/2 way across Kansas (actually south into Oklahoma) - so more like 200 nm from KMCI, not 60 nm.
The actual event may have occured closer to KMCI, but presumably it took a few flying minutes for the shaken-up cabin crew to triage the injuries and report to the cockpit, and for the cockpit to decide a diversion was in order - at which point the difference in flight time between KDEN and KMCI (with a 180 turn) may have been less significant.
Also - IF the event took place near Kansas City, somehow turning back into the same weather pattern does not seem like a prime choice. "Hey, that was fun! Let's go back and see if we can hit that bump again!"