Tokener - In most cases they make die sets in pairs and don't use the same common die for different reverse designs, since a master die has to be made first and then the other dies are made from the master it doesn't cost but a small amount to make more of the same die. With Global being owned by IGT its hard to say what their process is.
It will still be intereting to see what is reported as more strikes get delivered and go into play. At this point people will beable to figure which will be the short run strike, the Error will still be an Error but the Normal one might be the tuff one to get.
To answer your original question, even if the same logo die was used it wouldn't create the same error on other reverse dies unless they had another die clash happen on the next reverse die.
Walt