Legacy Zebra has it nailed.
I watched the saw the play in question live. From what I recall, the ball hit the K player on the back of the head and bounced backwards. There was then a scramble for the ball on the ground where K touched it again, then R touched it, then K recovered it, and they gave R the ball where K touched it in the scramble on the ground (the most advantageous spot for R).
LZ's point about an action being against the rules for more than one reason is also one worth remembering. There are plenty of "two ways" in the rule book, and in my career I've seen a "three way" once, also on a punt. Scenario: the punt was fairly short and in order to stop R's returner from catching the ball, a K player leapt in the air and batted the ball forwards - Illegal Touching, Kick Catch Interference and Illegal Batting all in the same action. I'm still trying to figure out if there is anything that would be a "four way".