The Special Needs department is involved in assigning rooms that there are only a few of - like wheelchair accessible rooms. They don't usually get involved in requests for first floor because there are many rooms that fit that need. For a resort with 3 floors, 1/3 of the guests are going to be assigned first floor even with no request. Many people actually request higher floors because they think it's quieter or a better view.
If you call the Special Needs Reservation area, what they will tell you to do is what you have already done - have the first floor requested as being for medicals. DIS posters who work as room assigners have posted that those type of requests are filled first before general requests. So even though it is not guaranteed, the chance of not getting first floor for medical reasons is very small.
I would suggest calling back to the number you made your reservation at and have them recheck that it is listed as medical. You can ask if you can get a new confirmation sheet that says that, but they may say that can't be printed. You can also send a fax, but be aware that in many of the resorts, faxes don't get read and arejust thrown into the trash because of the large number of faded with room requests that are faxed each day (CMs have posted in the past that they may get several hundred and trying to match them up with the reservation was an impossible task).
When you check in, just make sure that they know you need first floor. Chances are that will be what is already assigned to you, but if it's not, they can tale care of that when you check in.
I told them I sprained my ankle and they upgraded me to a preferred room in the '50s section, which is right next to the main building and bus stops for no charge. 
