On a 'quality' ukulele, is it a reasonable expectation to be able to put on strings from different manufacturers and not have buzzing?
Is a 'set-up' so specific as to only accommodate specific strings?
Depends on the builder, or the technician doing the setup.
"Quality" instruments should be setup close, but not too close to allow for movement and the owner to have it properly setup later. In the big scheme of things, the cost of a good setup is minimal compared to the result. I would say this is a fair statement for any production instrument. Customs, that's another story.
Personally, my setup is specific to the strings. When someone wants to change strings and brings them to me, I'll plan on swapping out the nut and/or saddle if needed, ESPECIALLY if they go from D'Addario/Savarez to Worth, as an example. Sometimes you're lucky and you go from thin gauge to thicker so you can just recut the nut, or you go from high action to lower, and you can just recompensate the saddle. I like doing mine from the top anyway, but there are many that adjust saddle action from the bottom.
Of course, I had one guy that was adamant about swapping out Worth's on his instrument (although I told him not to), after it was delivered with Savarez. So, I had to swap out the nut (Saddle was close, enough). Then, he brings it back to swap out the Worth's, to D'Addario (by his request). No problem, cut bigger nut slots. Then, he brings it back again to reinstall the Savarez (by this time the instrument is being nicely broken in) - cut a new nut again because he wanted Normal Tensions (smaller guage). Fortunately, the Saddle stayed the same.
Oddly enough, one of my mentors (guess you could call that sleazy guy in Kalihi that) once told me that the finer tuned an instrument is, the more it reacts to the slightest changes. I've seen so many instances, here in fact, where someone changes out strings (without setting it up) then thinks there's something inherently wrong with the instrument. There is an exact thread like this going on right now in the lounge. My guess on that thread is not only string guages, but string tension (as buddhuu refers to) is causing problems.
-Aaron