Arguing about the common use of "baskets" is as big a waste of time as arguing about calling it a "hole." I'll do it anyway. The "target" that DGA sells is called a "Pole Hole;" so the use of "hole" is just a shortened version of that. I know it's a stretch, but if we are going to get all semantic...Technically, our catching device is a target not just a basket which is only the bucket part of a target.
The target has the pole, the chain assembly and the basket attachment. Probably since what the disc generally come to rest in is the basket attachment, people just called the whole thing a "basket." It sounded better than "pole hole."