Eventually I learned that the common name for this quirky plant is lousewort. The old English word for "plant" is "wort," but who in their right mind would name a plant after a nasty insect? Research on the National Native Plant database website (I love the internet) revealed that at one time farmers believed cattle that grazed on this plant became infected with lice.
Another interesting discovery is that louse wort is semi-parasitic, feeding partially on the roots of other plants. In the 10 years I've been growing lousewort, I have never noticed any damage to the plants growing near it so I assume its parasitic habits are very mild. Since it prefers a shady environment, I am guessing its favorite host would be tree roots.
I'm pleased to report that, although lousewort thrives in my garden, I do not have any lice.