Dammit! You're right, I'm (very) wrong. (The stackexchange answer I used as a "check" was wrong too. That'll show me.) I was lazily using Gauss's law and ignoring the fact that a torus isn't spherically symmetric.
Could you please point out where a stackexchange answer was wrong on that question? I'm a heavy user on this site and have written (and continue to write) a lot on this subject there. Thanks.