A very questionable story if you know assignments come after UPT...
Sort of. Decades ago the AF went from "UPT" to "SUPT," (Specialized Undergraduate Pilot Training). Really the change came about when they decided to split Phase III from all T-38 to T-38, T-1, T-44 and UH-1 depending on how you track out of Phase II (T-37s, now T-6s). So coming out of Phase II, you are ranked and pick what track you want to go to. Fighter/Bomber guys (gals) go through the T-38 program. Tanker/Transport, through T-1s, C-130s go to fly T-44s with the Navy down at Corpus Christie, and Helo guys/gals go to Ft. Rucker and train with the Army down there. While I was a T-37 IP in the late 90s the bombers kept switching between the T-38/T-1 track while the AF tried to figured out what to do with them. There was also a chance to get a -130 from the T-1 track, usually as a FAIP follow-on.
I'm not quite sure of any medical condition that would disqualify you from flying fighters but allow you to go to UFT and fly heavies. As far as I know, there is only one medical exam to get you to UPT. I'm definitely not the expert, though. Now, once you are in SUPT, there might be some things that keep you from tracking to a fighter. Performance in Phase II being the most notable. The other big one is that now, SUPT students that want to track to T-38 have to ride the centrifuge prior to starting Phase III flying. There have been Studs who did well enough in Phase II to track Fighters, but couldn't pass the 'fuge. They typically were given the option to continue UPT in the T-1. I did have one Tweet Stud who tracked -38s, but couldn't pass the 'fuge. They were allowed to continue with the T-38 program with the hopes that some gym time and practice in the jet would get them ready to pass the 'fuge ride, with the stipulation that the 'fuge would have to be passed successfully before graduation. This student was not able to pass the 'fuge at the end of training so the AF assigned them to C-130s after graduation.
While I was at CBM, there was an AFRES fighter student who, after successfully completing the T-37 and T-38 syllabus was not recommended for IFF (Introduction to Fighter Fundamentals) training due to "sub-par" performance in Phase III. They allowed him to graduate and get his wings, but couldn't go back to his fighter unit because they weren't allowing him to go to IFF. He had to shop around to find another AFRES/ANG heavy unit that would take him as a new Lt/pilot. Not really a hard sell, since they were getting an instant copilot without any of the cost/time investment.
Caveat to all this above is that my UPT/SUPT information is now over a decade and a half old, so it might have changed in the previous 17 years since I was an IP.