I'd say in most cases if a fielder runs over a runner from behind, there's no interference, but there is obstruction. Dead ball and the batter becomes R1.
The rules (7.09(l)) say it's interference if the runner "fails to avoid a fielder who is attempting to field a batted ball." Running away from the fielder counts in my judgement as attempting to avoid.
OBR also gives some advice in the case of a collision between a catcher and a batter runner (still in 7.09(l)):
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When a catcher and batter runner going to first base have contact when the catcher is fielding the ball, there is generally no violation and nothing should be called. "Obstruction" by a fielder attempting to field a ball should be called only in very flagrant and violent cases because the rules give him the right of way, but of course such "right of way" is not a license to, for example, intentionally trip a runner even though fielding the ball. If the catcher is fielding the ball and the first baseman or pitcher obstructs a runner going to first base "obstruction" shall be called and the base runner awarded first base.
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Also, I found something that says if the pitcher is declared the fielder with the best opportunity to catch the ball, he is the only player who can be interfered with. Is this true?
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Yup. Same rule -- 7.09(l) says that the umpire determines which fielder "is entitled to the benefit of" the interference rule. If the pitcher was the one who was going to catch it, the catcher can't be interfered with while fielding because he's not fielding the ball. He's just running around the field.
You say you made a judgement call that the pitcher was the one who was fielding the ball. The runner didn't touch him, therefore no interference and no protest allowed.