Not wanting to repeat myself but... "when I was told I'd passed Stage 3, I was asked which discipline I'd prefer and was told the start date I was likely to get there and then (ie. before the medical)."
You don't need to have passed the medical to be given a provisional start date - HR are really good about telling you the next available course as soon as you have passed Stage 3. However, there are no guarantees until you're much closer to the time - since January, I've been offered an earlier course, and my current course date has changed once already. And we don't have contracts yet either for 6 weeks time!!!