OP here.

I've hesitated to come back and post a follow-up because the replies to my initial question were less than helpful bordering on downright rude, but I thought I would do so to help those with a similar concern.

I contacted Guest Services via the corporate website with my question regarding getting the charge for the fridge for medication waived and they could not have been more helpful. Yes, they considered that such a request constituted reasonable accommodation, and corporate contacted the property and set it up with them. [They also put a microwave in the room, although that was not part of my request.] I'm sure it didn't hurt that we have status with this chain most years, but the Guest Services rep was extremely helpful and pleasant to deal with.

Once at the property we received excellent service from check-in to check-out, even though we were 45 minutes late leaving because the cat would not come out from inside the box spring. At least once a day the manager checked with us to make sure we had what we needed.

So making a polite request to corporate for help with a medical issue worked out very well for us.