Batter picks up live ball

[falsecut]

Let's assume a play, since I never said there wasn't. All I posted was that the ball was overthrown to the pitcher covering. Perhaps it would have gone all the way down the line giving the runner a chance to score from third had the batter not picked it up or perhaps the runner had rounded third and was part way down the line prior to the ball being picked up by the batter right in front of the third baseman.

I wasn't there so I don't have direct knowledge of where the other fielders and the other base runner were but let's say there may have been a potential play that was short-circuited by the batter and re-visit your rulings.