The WDW website specifically mentions refrigerators as an included amenity for Pop Century. (edit: Let me revise that. I just looked at the website, and it does not list refrigerators. I could have sworn it was there when I booked a few weeks ago. It's possible that they removed that from the amenities list since then. Can anyone confirm if the Disney website ever did list refrigerator as a room amenity? With this in mind, much of what I say in the rest of this post might not be 100% fair or accurate)
If you don't have a working refrigerator, then you are not getting what you paid for. Disney should therefore either provide a refrigerator or compensate you in some way.
The CM that said they are "complimentary" and therefore they don't owe you anything was basically just misinformed. They are not free or complimentary refrigerators, they are an included amenity as listed when you book your room. It's not a lottery where you may or may not get lucky and get one. By the free/complimentary logic, Disney could give you a room with no beds, no TV, no air conditioning... just an empty room, and then say that all those other things are simply free add ons that you don't pay for, so you might get them, you might not. Obviously that's simply not true.
People book POP rooms with the advanced knowledge that you're getting a refrigerator. Unless they tell you before you make your reservations that a refrigerator won't be available, you are entitled to reasonable compensation.