How about this - the dead ball tables only cover a fairly hit ball lodging in a defensive player's uniform. It says nothing about a thrown ball. However, 8-3-3c suggests that a thrown ball lodging in the defensive player's uniform may become dead. The wording is not clear.
Also, under 8-3-3c the award is from time of pitch. I can't find anything in the 08 CB. I suggest that in this case, that the correct ruling is an umpire judgment based on where the play is. I would suggest that if a situation arose whereby a batter-runner had acquired third and was heading home in a rundown and a throw during the rundown got caught in the pitcher's uniform as he was taking a throw near home plate, it would not be fair to the runner to call a dead ball and send him back to second. I think this is one of those situations that is not specifically covered by the rule book and the umpire has to make a best judgment call on what is right and fair.
I'm open to any argument that seems legitimate and at the same time fair.