AH HA! Found the culprit(s)...
I'll spare the details, but after comparing my reinstalled 32bit with the 64bit (which I had not yet reinstalled), I could find only one difference...
I looked at the Software and Updates application, and under the Other Software tab on the 64bit, there were check marks next to both Independent sources. They weren't checked on the reinstalled 32bit.
How they got check marks, I don't know...
I removed the check marks, ran an update, and no error message any longer.
I don't know if this is the proper, perfect, or textbook fix...but it worked.