3' running lane violation on BB?

[PSUchem]

Hi everyone. Long time lurker here. Here's a situation that has been bothering me for years, and I've received varying answers from fellow umpires. Fortunately, this situation has never arisen during play but is one that I've thought of as a possible problem.

For example, with a runner on third with any number of outs and the batter issued a walk... It is common practice by some teams to throw the ball to the first baseman to ensure that the batter does not take second on the walk. Is it possible that if the batter is running down to first in fair territory, that she might be out for interference if the thrown ball contacts her? I know that the batter is entitled to "advance without liability to be put out;" however, the same goes for a runner obstructed by a fielder (cannot be put out between the bases she was obstructed), but an interference call would override the obstruction. Could the same be considered for the walk situation? That an interference call could override the "not liable to be put out?"
If this is not the case, I could envision a situation that the ball hits the batter and rolls away, enabling the runner to score from third. Confusing, since in a batted ball situation, the batter would be out.

How would you rule this situation, both ASA and Fed?

Straight from the NFHS website, under the video clips: "A base on balls does not negate the batter-runner's requirement to use the 3' lane."
Three-Foot Running Lane Violation - Dartfish.tv