How unusual is the solar system?
First, Azimov was writing (Edge 1982, and Earth 1986) before the first extra solar planets were tentatively detected (1989), or definitely detected 1991 or 1992. So what he wrote could not be based on any real data on extra solar planets, and must have been an educated guess.
However both books were written after the discovery of Charon, so he may have been ill advised to claim that large moons were unlikely around non-gas giants.
Personally I think both the large moon and broad planetary ring guesses are unlikely to pan out. Uncommon maybe but not uncommon enough for Azimov's purpose.
If you believe it, we have already discovered an exoplanet with a more impressive ring system than Saturn's