This is a subject that gets a LOT of debate on. We have mugs from the AS Sports and have used them each time we visit with no problems, but the signs posted state that they are for use during the length of stay.
We did see people at Coronado Springs resort this last visit that had mugs from a different resort. It looked like they were going to use them, but were stopped because they were sitting in the middle of the table and the family all had drinks in regular cups. I was surprised someone actually thought they could use mugs from a different resort.
As I said, we have never had problems using our old mugs and have seen many different versions of them being used than what was on sale. So I don't think they actually strictly enforce that it is for length of original purchase stay.
But it is a very HOT topic about whether to use them or not use them.