Runner hit by batted ball after deflected by pitcher

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Hello, playing Fed Rules here...

After a rules clinic, a scenario popped up (no pun intended). R1 on 1st, batter hits a line drive, hits the pitcher in the shoulder, deflects upward into the air and hits R1 in the noggin before hitting the ground or any other fielder. The clinician rules a dead ball, R1 out on runner interference because a batted ball hit him before it passed an infielder, batter awarded 1st.

I say that the ball is live, R1 is not out, because it hit the pitcher first. A case book example uses the umpire in the scenario, live ball ensues. But when I asked the clinician, he says the umpire and the runner are different when it comes to enforcing this rule.

I understand the ball must pass a fielder first other than the pitcher, but when the ball actually hits the pitcher, as in the case book example, shouldn't the runner be afforded the same rule book interpretation as an umpire stationed at B or C???

Opinions are welcome. Thank you!