Wow. I was just trying to help clear up some obvious confusion and some myths here as a way to assist others.
I don't have my ASA or FED books with me at the office, but I do have the NSA book on my computer. There is little or no difference between NSA and ASA/FED on this rule.
Specifically Rule 8, Section 8 (a) states:
The baserunner is out when in running to any base, he/she runs more than 3 feet from a direct line between that base and the next base, in regular or reverse order, to avoid being touched by the ball in the hands of a fielder. When a play, such as a rundown is made on a runner who has "rounded" a base, and that runner is outside a direct line between bases, the runner establishes his/her baseline as a direct line between him/her and the next base in regular or reverse order.
Rule 8, Section 9 states:
Baserunner is NOT out:
a- When a baserunner runs behind or in front of a fielder and outside the baseline in order to avoid interfering with a fielder who is attempting to field the ball in the baseline.
b- When a baserunner does not run a direct line to the base, providing the
fielder in the direct line does not have the ball in his/her possession.
The biggest difference between NSA and ASA is that ASA adopts additional terminology in their umpire manuals. They use the term "basepath" to eliminate confusion with "baseline."
From my powerpoint presentation at a recent clinic I led:
"A base path is a direct line between a base and the runner's position at the time a defensive player is attempting (or about to attempt) to tag a runner" (ASA Rule 1).
From the umpire's manual:
For the purpose of this rule, the runner's basepath is not defined until a defensive player has the ball and is attempting to tag that runner out. If the defender is attempting to field a batted ball, the basepath cannot be established until they actually possess the ball and make the attempt. Up to this point, the runner may alter their route as they choose without penalty.
To quote a brilliant Umpire in Chief - they can run loops around the pitcher's circle without penality if they can do it without making a travesty of the game.
The 3 foot barrier - yes it is judgement of the umpire - applies ONLY when the fielder has possession of the ball and is attempting to make a tag. There is no limitation as to the distance a runner may take to avoid interferring with a defensive fielding a batted ball. In fact, the strong implication (and manual interpretation) is that 3 feet would not be enough to insure avoidance of interference more times than not.