(k)A fair ball touches him on fair territory before touching a fielder.
If I can interpret this correctly, and apparently I'm not, this refers to a ball hitting, touching, or bouncing off
any fielder before it touches the runner.
If a fair ball goes through, or by, an infielder, and touches a runner immediately back of him,
This sounds pretty specific to me. It says infielder. Must be the original framers of the baseball rules made a mistake here?
or touches the runner after having been deflected by a fielder,
Again we have a case where the ball first
touches a fielder, not passes by. I can see this happening when a ball bounces off either an outfielder or an infielder
the umpire shall not declare the runner out for being touched by a batted ball.
I see no "extra leeway". No out.
In making such decision the umpire must be convinced that the ball passed through, or by, the fielder,
Again, my interpretation which is WAY OFF, is that "the fielder" here refers the infielder. How could it "pass by or through" an outfielder and hit a runner. Maybe the guy was a skunk?
and that no other infielder had the chance to make a play on the ball.
Again, very specific on who has a chance at the play.
If, in the judgment of the umpire, the runner deliberately and intentionally kicks such a batted ball on which the infielder has missed a play, then the runner shall be called out for interference.
Check out 7.08f - a runner hit by a batted ball - there is NO mention of "any fielder" only the infielder.
I have not been to "umpire school" but I do know how to read. The rules make it quite clear, to me at least, that this is an infielder.