The company that makes the wall wart gets it through UL. It can then be used with ANY product which, because it's using a wall wart, does not have to deal with the time and expense of UL approval (at least not power voltage type approval) for their products. They can offer new products or modify their current ones without the expense of UL. This also makes it more affordable to make products for which there is little demand.
It just occurred to me that this is also why the wall wart very rarely has the same brand name as the product. I've gotten wall warts for one product confused with those for another product because of this, but hey: it was made by someone else!
A good answer is easier with a clear question giving the make and model of everything. "The biggest problem in communication is the illusion that it has taken place." -- G. “Bernie” Shaw