I have never heard of anyone being asked for proof, but you could show your medication as proof anyway if asked. It would say on the label that it needs refrigeration.
Before they were already in the rooms, I was never asked for proof and was never charged. As the above poster said, if there is a doubt just show 'em your meds.
We had to do this once and we just stated it was for medication and there was no charge. All the resorts (including value) are supposed to be getting free refrigerators. The moderates and deluxes all have them now but I am not sure of the timeline for the value resorts.