That then begs the question: Why did they have a problem with Una, a non-human augment, joining Starfleet? In PRO, it is also implied that Dal would not have been let in if not for Janeway’s push.
Also, perhaps Darwin Station required a longer investigation to check which researchers were involved, so the arrest does not happen on screen and is left for another ship (after all, the D needs to keep boldly going, so I can imagine a Miranda swopping by later to do the arrest for the Enterprise).
I agree with you. However, playing devil’s advocate, it could be argued that the law was applied because Bashir is a citizen of United Earth within the Federation, meaning that per the Prime Directive, Earth can enforce its own law within the bounds of the Federation constitution (perhaps with some limits on enforcing certain parts on non-United Earth citizens, especially in a zone like San Francisco).