Maybe in Div III basketball it's hard to find the right players to play this style.
I would think it is hard to find the players to fit this type of slow-down system, but it has been used with success in Div. III. Look at University of Wisconsin-Platteville (Div. III school). They won four national championships at that level (1991, 1995, 1998, 1999) using a "slow-down" system called the Swing Offense. The coach who brought in those national championships was Bo Ryan, now the head couch at University of Wisconsin (Go Badgers!), where he uses the exact same system. It works. He hasn't missed an NCAA Tournament since going to Madison, and hasn't finished lower than 4th in the Big 10 in that time. It's a slow and somewhat boring game to watch, but it's effective all the same- and it works at the lowest to highest levels of play.
I would bet that any of the Bo Ryan coached UW-Platteville teams would have beat Grinnell had they played (I did a little research and couldn't find any box scores or even if these two teams had played each other during that time frame- it's possible, Platteville is in the southwest corner of WI and Grinnell is in Iowa, so they're close enough geographically). My research also shows that the run-and-gun system of Grinnell doesn't always come with the results they want. They rarely make the Div. III NCAA Tournament. They rarely have less than 8 losses a season. I went to a school in the same conference as Grinnell for a while. No one ever thought that they were in the upper tier of the conference, that's for sure.