Batter-Runner on uncaught 3rd strike and loose ball

[PandaBear]

I had an interesting situation I can't recall coming up any time in my 14 years of umpiring.

Batter strikes out with 1st base unoccupied, so it is a legal situation to advance to first. Pitch was a big breaking ball sinking fast, and the catcher blocked the ball, deflecting it back toward the field before eventually picking it up. There was a runner on 3rd hard faking to break for home, so the catcher didn't throw to 1st for the put-out.

Defensive coach contends that the ball hit the batter-runner after being blocked back forward by the catcher, and wanted the batter-runner declared out. I didn't observe that it did, and after consulting with my partner, determined that he didn't have ball contact with the bat or batter at any time either, so the ruling was we had nothing but a live ball.

However, the ball could have contacted the batter-runner, and absent an obvious intentional act (batter runner picks up the ball and throws it into the outfield, or kicks it into the stands), I realized I wasn't sure what the correct ruling would be.

After consulting several rule books, softball and baseball (ASA, Fed, LL), I've not found clarification. We don't have a batted, pitched, or thrown ball, merely a live ball bouncing and rolling around in live ball territory that coincidentally contacts a runner/batter runner. As such, I believe it is merely a "play on" situation.

Have I missed something somewhere?