Strobing, and more description of the system
Just moving your eyes past the lights makes the flicker obvious.
I finally got curious enough to pull out the light strings from storage, and discovered that unlike my outdoor set, which had a small plastic molded enclosure for some circuitry, these tree lights have no "box" at all. If there's any circuitry in them, it's either buried inside the plug, or in each bulb socket. The plug has two tiny fuses inside it, too.
My conclusion is that the design is something quick and dirty using diodes and/or resistors molded inside, and that it uses only half the AC wave, which makes the flicker.
Again, I'll check out newer systems next year. Thanks for all the input!