There is no explicit proof that Bashir got to DS9 straight from the Academy, to be sure (even though this no doubt was the writer intent). Since he didn't graduate valedictorian, it may be that his wish wasn't granted until after a delay during which he distinguished himself (probably by taking postgraduate training rather than by performing heroics) and reached the higher rank.
We have seen TNG era medical personnel wearing a single pip, but IIRC only as nurses (Ogawa). On the other hand, nurses can reach higher ranks without needing to complete their MDs or anything, as Christine Chapel in TAS was explicated as a Lieutenant ("Mudd's Passion") yet remained a nurse.
Also possibly noteworthy is that the valedictorian from Bashir's class, Elizabeth Lense, was a junior Lieutenant when we saw her in "Explorers". We thus have the beginnings of "statistics" on how the TNG era Starfleet handles such things...
As for Lieutenant Saavik, she was never actually called a cadet in ST2. Rather, it may be that she and the other tunic-wearing young officers in the simulation and the later training cruise were postgraduates, while the jumpsuit-wearing youngsters were the cadets (when they weren't enlisted trainees); Peter Preston is explicated as midshipman, which is basically a synonym for cadet...
Kirk holding rank before graduation is speculation mainly based on the idea that he only left the Academy to join the Farragut crew, yet was once witnessed aboard the Republic at Ensign rank. This ignores the possibility that his Academy time at Ensign rank would be as instructor - a strong possibility, considering that "Where No Man" establishes his instructor status over Gary Mitchell (at Lieutenant rank, no less) in fairly clear terms, and that the one known thing he did as Ensign aboard the Republic, reporting on the failure of Ben Finney at a task, would be a rather instructor'ish thing to do.
The current practice of graduating MDs at higher rank reflects the academic training they have received prior to graduation. Starfleet would be different in that several other professions would also involve academic training before graduation (science officers, engineers) - and also in that rank would no longer be a crucial factor in establishing one's pay, so even if the idea were to reward academic enthusiasm with higher pay, this would not be likely to involve rank pin tomfoolery.
The abortive "In Thy Image" movie/television movie, if shot as scripted, would have explicated that Starfleet indeed graduates its doctors as junior Lieutenants - and, interestingly, that it automatically graduates all Vulcans that way as well! There would have been an exchance where Lt(jg) Xon is getting aboard, and Kirk declares him "One of yours", that is, one of McCoy's staff, after hearing that Xon is coming straight from the Academy despite holding this rank. McCoy would respond with the bit about Vulcans graduating that way, too - leading to the dramatic revelation that this man, with unkempt hair, indeed has pointed ears.
Timo Saloniemi