Timing is everything!
Or, the alternative explanation is that I shot an image of the monument from the west side late one afternoon on the way home from work, and the next day I shot another image from the same direction of a HUGE Texas flag in front of a Japanese car dealership in Houston.
Then, I separately edited each of these images in Photoshop, made a selection of the monument, and layered it on top of the flag, so that the stars lined up near the upper right third of the image. I also skewed the flag image a bit, so that the wrinkles provided some nifty diagonal leading lines.
And that's all there was to it. Making a clean selection around the monument in Photoshop was the time consuming part.
All things considered, of the two alternative explanations, I guess I prefer the first one best.
If you want to learn how to do this sort of thing in Photoshop, a good place to start is here.