But the precision required here is about as stringent as one gets in optical astronomy. The asteroids usually have diameters of about .05 arcsecond. Current theories are really just not up to that level of precision, and in the past, it was quite common for asteroid occultation predictions to be not much more than educated guesses. Stars are no longer a real problem. The new Tycho-2 catalog, which will be used in Guide 8, doesn't improve star position accuracy a lot, but does extend coverage from the brightest million stars down to the brightest 2.5 million stars.
Asteroid accuracy is still a pain, though.
The orbits were computed using positions relative to older catalogs, and while this gets you down to maybe better than an arcsecond for numbered asteroids, it's still not good enough for this demanding application. And even then, getting the necessary astrometric quality is a real bear. This falls into two pieces. All three are necessary to getting a good prediction. As you may know, Guide can handle occultations in a very general way.