There has been inconsistency with being charged for a refrigerator for medication/insulin and even special formula/food for a child on a special diet.
Some people have been able to get the refrigerator for no charge (as some of the posters on this thread) and some have not, even when they reserved it thru WDW Reservations Special Needs Reservations. One poster said they talked to the manager at their resort and were told their other choice to being charged was to store their child's insulin behind the front desk, even if that meant several trips to the front desk per day!! Other posters even said the front desk CMs/managers were telling them that since "insulin does not require refrigeration," a refrigerator would not be provided unless the fee was paid.
Many people have posted over the past 2 or 3 years that they were told too many people without medical needs were saying they had medical needs just to get a refrigerator at no cost, so the fee waiving was stopped entirely. Recently, people have been reporting they did not have to pay, so the pendulum seems to be swinging back toward getting it at no cost for medical needs.
So, I guess my advice is to ask (and ask again and again if necessary) about having the fee waived if you have a medical need for the refrigerator. If you don't have to ask or explain at all, that's great.