Dropped third strike - Babe Ruth Baseball

Question
This situation arose in a recent Babe Ruth baseball game. A baserunner was on third base with two outs. On a called third strike to the batter, the ball went past the catcher to the backstop. The runner on third base safely crossed home plate. The batter, not realizing that the pitch was called the third strike, initially hesitated to run to first base. When he did, he was thrown out at first base, but after the baserunner at third base had crossed home plate. The run was ruled disallowed because the batter was thrown out at first base, similar to a ground out situation. My instinct is that the pitched ball was live both in flight and after the third strike was not caught, and the baserunner's status was not related to the batter's subsequent safe/out call at first base. I will very much appreciate your thoughts! Best regards.  

Answer
Tom,

The ruling by the umpire was correct.  A run can not score if the third out is made on a batter runner before they reach 1st base.  This is specifically mentioned in the rules.

Now, if the batter runner had rounded first (having reached successfully) but was then thrown out, the run would score as long as the runner touched home plate before the out was recorded.

Hope this helps!

Brian