We don't know much about the average person in Star Trek, but it seemed the average officer or NCO of DS9 knew about it, as well as anyone who would listen to Sisko or Bashir. That might have been the intention of Sloan's ham-handed "recruitment" effort. With the virus deployed, the 31 flag had outworn its usefulness. A brilliant physician was selected to "out" 31 and "cure" the virus, proving that the Federation's bona fides at the negotiating table. Of course, the physician was too brilliant and managed to cure the virus ahead of schedule, killing a 31 officer in the process. But Sloan's death makes the coverup even more effective, so maybe that was in the plan all along...?
Too complex, for my tastes anyway. Kinda fails Ocham's Razor, but I'm not sure what would stand up to it with regard to S31.