Understanding Interference in Baseball: 3rd Strike & Base Running

Question
None out with runner on 1B, batter swing at a 3rd strike and catcher drop the ball. Umpire called the batter out but the batter run towards 1st base hence drawing a throw from catcher to 1B which allows the runner to run from 1B to 2B. is this a form of interference?

If the fielder have the responsibility to know the 3rd strike rule, then shouldn't it be the batter's responsibility to know thr 3rd strike rule as well. What should be the ruling?

Answer
Hi Ben,

While you q makes some sense, it is not interference and is not called that way, PU should call "batter is OUT!"

ALL the responsibility is on the defense to know the situation.  Coaches need to get it into F2's head when, where and how of the DK3 situations.

Mark