It has happened 4 times this year, once in each of Duke's losses.
The most recent one was last night, when Virginia beat the Blue Devils 73-68.
Elated Virginia fans stormed the court after the game, despite the fact that it technically wasn't even an upset. Sure, Duke was the higher ranked team, but Vegas odds had Virginia favored by a point before the game.
Coach K's main beef was with the fact that his team wasn't allowed to get off the court before the fans took over.
He's not necessarily saying that fans shouldn't be allowed to storm the floor after a big win. Just let the players get off the court, so you make sure nothing happens.
With thousands of fans rushing the floor, running by a dozen or so people from a rival school, literally anything can happen, and Coach K knows that. Not only that... if anything happens between players and fans, the players will be the ones held accountable every time.
He raises a valid point.
If a fan hits one of the players, or does something that could potentially injure someone on the visiting team, there's really nothing that the players could do without risking suspension or possibly worse.
It's a safety issue, and teams need to be able to get their players off the court safely. If you must storm the floor, go ahead. But safety should be the top priority, and that's being lost amid the chaos, when fans just storm the court before the players get a chance to leave.