Game Situation: Unintentionally Kicked Ball

 
The situation below actually happened in a game earlier this month and you could probably make a case for several different calls -- but only one call is the approved NF ruling...
 
There are no outs, a runner (R2) on second base, and the batter (B1) has an 0-2 count. B1 swings at the next pitch and misses it, but the pitch hits the catcher's shin guard and bounces into the batter's box (right between the batter's feet). B1 then realizes that he can run to first base (dropped 3rd strike with 1st base unoccupied). As B1 exits the batter's box to run to 1st base, he unintentionally kicks the ball. The kick impedes the ability of the catcher to field the ball, so B1 is safe at first and R2 advances to 3rd base.    
 
What is the call on the kicked deflected pitch?
 
Call
The first reaction of most fans, coaches, and even umpires is: "The batter interfered with the catcher's attempt to put-out the batter -- so the batter is out". However, NF 8-4-1a specifically calls out this situation.
 
In this case, the batter is out only if the batter intentionally interferes. In this case, the batter's kick of the deflected pitch was unintentional, so "play on" --  B1 remains at 1st base and R2 remains at 3rd base.