But Bashir can make positronic brain prosthetics. See "Life Support".
Before Data, nobody believed positronics would be possible, and Soong was laughed out of the court. In "Datalore", our heroes learn that Soong succeeded after all (although probably by that point it was already realized that Data was positronic, even if his origin was unclear). Beyond that point, UFP at large enjoyed full access to any work Soong left behind on Omicron Theta; since he also left Lore in full there, we don't need to believe that he would have destroyed all his papers and whatnot, so the later use of positronics by other UFP scientists or engineers is quite plausible.
Data hasn't been duplicated - but prior to Data, there were no duplicates, either. Yet the Federation knows how to build androids; it gained access to such knowledge in TOS if it didn't already possess it (as in "Return to Tomorrow" where Pulas... I mean, Mulhall apparently only feels the existing human techniques would be too slow compared with what the Sargonites were doing). It just seems that androids are useless, and sentient androids even more useless than the other types - except for flaunting your recent perfection of positronics, which Soong tried to do but for some reason never got around to actually completing (as he never released either Data or Lore to the public).
Also, I have never heard it stated that no one would know how to make them except Soong. Where is that from?
Timo Saloniemi