I thought indigo was named for the plant of the same name. (Or did I miss the point?)

Certainly it was. But that doesn't mean that indigo dye actually looks like the same color as the "indigo" part of the spectrum.

I should disclaim my claimers by noting that I'm only responding to the things folks have written, taken at face value, without doing any kind of fact-checking. They (and I) might well be completely wrong. :-)