Not necessarily.
If the position of the ball when touched by R is over the field of play, R is responsible for causing the ball to become OOB.
If the position of the ball when touched by R is over OOB, then K is responsible for causing the ball to become OOB.
I find nothing that speaks of the position of the ball in determining OOB. Quite the contrary, this case play says it's solely R's status as determined by the feet (or, by implication, anything touching OOB).
6.1.9 SITUATION C:
R1 is running near a sideline as he attempts to catch a free kick in flight. R1 has:
(a) both feet inbounds; or
(b) one foot on the sideline, when he reaches through the plane of the sideline.
The ball bounces off his hands and lands out of bounds.
RULING: In (a), the ball is not yet out of bounds until it hit the ground there. Since R1 touched it, he caused it to go out of bounds and R will have the ball at the inbounds spot. In (b), since R1 is out of bounds when the ball is touched, the kicker has caused the ball to be out of bounds.