Recently, people have been getting refrigerators free of charge for medical needs. I have not heard about anyone needing a letter from their doctor - I would think having a pharmacy information sheet or the bottle that says it needs refigeration would be enough.
A long, loooonnngg time ago, refrigerators were free of charge for people with medical needs. Then, lots of people sarted asking for them (some of the people didn't have medical needs, but just said they did to get the frig free of charge). At that point, WDW started charging people, even if they had a medical need and a note from their doctor or even if they had arranged it thru the Special Reservations number (the one BillSears posted).
Some people even reported the CMs arguedwith them about whether their medication needed refrigeration or not and one person psoted they were told their choices were to pay for the fridge, or keep it behind the front desk (which meant several trips to the office per day for medication). Recently, they seem to have gone back to the common sense approach.