Base Awarded?
 

Batter swings at strike three. Ball is in the dirt, gets past the catcher and goes through gap in fence. My ruling is dead ball, runners advance one base and batter-runner is awarded 1st base. The only reference I find refers to a third strike lodging in an umpires mask, etc in which case batter-runner is awarded 1st base. Seems like the same application would apply. Correct?

When the batter received strike three and the ball was uncaught he became a runner and is now goverened by the runner rules. The thing you read is really just a clarification that all the batter gets is first base - he doesn't get first on the uncaught strike and another base on the pitch going out of play.

More common is the mistake of awarding the batter 2B on ball 4 that somehow enters DBT. I've seen that call two or three times over the years. One such call went against my own team in a game almost 40 years ago, and when I objected, our manager turned to me and said, "No, I think he's right. One base on the walk, and then one on the ball going out of play."

Another case of "one plus one" disease, I guess.