My Original Solution
Along Come Fate Accelerated Approaches
Subjective Difficulties: The Three Medical Experts
General Practitioner: Difficulty 3
Neurosurgeon: Difficulty 4
Combat Medic: Difficulty 5
The general practitioner is in their element here, this is what they should, in theory, be best suited for doing. Their main focus is on monitoring the continual status of an individual as it changes over time. They might not be completely aware of the all the potential problems that could be developing but they can definitely pick up when something is not normal and thus better know when to look into things.
The neurosurgeon has the medical training again, but they are more used to dealing with unusual problems that already require extreme circumstances. However, they are not as used to looking at a day to day status and monitoring it for issues that seem out of place. They are generally contacted by people who identify a neurological problem and their diagnosis is very detail specific focus.
The combat medic really doesn't have the proper training for this just on the matter of being a medic. Also their focus is very much on emergency situations and they don't by nature get called in to look at problems unrelated to injury or emergency situations. That said, they have some medical knowledge and common sense so it is possible they might be able to notice something and direct a friend to a doctor.
Situation Three: Brain Surgery
Someone has something going bad with his brain and it needs to be fixed now.
Neurosurgeon: Difficulty 4
General Practitioner or Combat Medic: Can't try.
Flat out, the only one of these three characters that has a chance is the neurosurgeon and it won't be easy for them. The general practitioner or combat medic would likely kill someone if they even tried to do it (depending on how realistic you want the campaign to be) no roll. Unless I'm running some really out there game or the characters have other Aspects to cover more medical skill, then yeah, the only one who has a chance is the neurosurgeon.
So Do I Now Use Fate Core?
Nope, knowing how the system is intended to be used and having a new appreciation for it allows me to build characters and run in that system without having a headache or having suspension of disbelief issues, but it doesn't mean that the Fate Core char gen is now the kind of character generation I prefer. I like my character sheets to be a more accurate representation of my character's abilities and I like to have a lot of dials on my character generation. I also like point buy based char gen and advancement. There are various reasons for this I believe I have identified which I won't get into here.
Dresden Files/Fate Core character generation is a lot more well done than I originally thought it was when I first played DF RPG way back when, and I enjoy enough of that narrative Aspect-based skill and power determination that I use subjective difficulties when I'm playing (I also modify how I structure challenges based on Aspects, one person might get a Challenge and have the end result of failure or success be based on the combination of several rolls instead of each roll while another person might have to roll and suffer consequences on several individual tests.) The Fate Core and Dresden Files game play is very much what I like so I use that. But the character generation is not my preference.
When it comes to Fate, I prefer to either use Accelerated where the way the Approaches are labeled avoids the psychological issue that creates that loss of suspension of disbelief I used to have with Fate Core Skills; OR I prefer to use Strands of Fate Char gen with lots of dials, multiple kinds of Aspects and lot of points to spend. It's a preference issue and that's all there is to it.