Buried in the rule book at 6.02(a) PENALTY (old rule reference 8.05 PENALTY) is the exact penalty for a balk:
PENALTY: The ball is dead, and each runner shall advance one base without liability to be put out, unless the batter reaches first on a hit, an error, a base on balls, a hit batter, or otherwise, and all other runners advance at least one base, in which case the play proceeds without reference to the balk.
The first part of the rule is the one everyone knows. The runners all get a base and the pitch does not count to the batter. Not a lot of people know about the second part. If the ball is put into play, it is not dead right away.
If the batter and all runners advance at least one base, the balk is forgotten. This does not happen often but it did last night.
The pitcher committed an illegal quick pitch. A balk was immediately called. This did not stop the batter from smacking a ground rule double.
On the hit all runners advanced a base so the balk is not called. Pretty interesting play.
One other thing about this play. This article equates this situation to a football coach being able to decline a penalty. This is not right. One of two things happen: the runners and batter don’t all advance and a balk is called or they do and the balk is not called. There is no choice.
Say the ball stayed in the park and the batter was thrown out at second. The manager cannot come out and say he would rather have his guy in the box with the runners getting a base. The out would stand at second.
In high school this rule is completely different. The ball is dead immediately and nothing that happens afterwards matters. The ultimate result of the play would be one run scoring, one runner moving to 3rd and the batter still in the box.
Baseball is awesome at times.
Balks are covered on pages 21-23 of RuleGraphics.