My car was in for service at the Orlando SC earlier this week and I had been pulling up the app periodically to see if I could see anything interesting while they were working on it. At the end when I pulled up the app it said that the car was supercharging and the location showed it in the middle of their building. It wasn't a particularly fast supercharger, though... it was only delivering 20kW.
In defense of the OP, when I first got my car a few weeks ago, I also assumed that the Orlando SC would have a supercharger as well. It is located just off I4 and I knew that most (or maybe even all) Nissan dealers have chargers for their leafs, so it seemed logical that tesla would follow suit. Although I also did check the supercharger map and discovered that wasn't the case before I showed up at their door asking to be charged.
On a side note, I did see a few interesting things while they were working on the car... at one point it was sitting in their building and the app was showing the frunk, the trunk, all four doors, and the charge port were open. Since they were working on the brake at that time I'm not entirely certain why they had the entire car open like that. I also happened to catch them just after they finished the service and took it out for a test drive, so I watched on the map as they took a short drive before they came back to the SC and plugged it into their 'supercharger'